I find the argument to be random but there is about a 100% probability that aliens exist.
On Aliens

According to cosmology, the part of the Universe that we can ever reach or communicate with only contains a finite amount of matter and energy, about a hundred billion galaxies worth. So for practical purposes the Universe of which we can gain direct knowledge is not infinite, just large.
Bayesian arguments are appropriate. Let's assume the Multiverse concept is true and there are a vast number of other parts of the Multiverse analogous to our entire observable Universe, but with variations of all types, including of physical laws.
We have one key piece of information: that there is at least one example of intelligent life in our observable Universe. In Bayesian terms, this restricts our branch of the Multiverse to the ones where there is at least one example of intelligent life (i.e. excluding all the ones where there are zero). The question for a Baysian analysis is what is the distribution of the counts of intelligent life across all of the Universes with at least one example.
If where life is possible, it is pretty much an inevitability, there will be very few Universes with just one example of intelligent life. But there is another possibility. This is that in the Universes where it is possible for intelligent life to develop, it requires an exceptional fluke for this to actually happen. This is quite plausible, since we know intelligent life failed to occur on Earth for 4.7 billion years (this is true even if you count mammals and birds as intelligent).
There are many ways this can be so. It may be that life itself requires a huge fluke, or complex multicellular life requires a huge fluke (this is the best bet, as it took the longest - a few billion years).
Anyway, the bottom line in this picture is that it might be that of the Universes in the Multiverse, most have no higher life and a few have one fluke occurrence of it, with far fewer having more than one example.
Sorry, but this is the way it may be.
Perhaps this analogy will help. You live in a remote house with little knowledge of the outside world and a meteorite falls through your roof. You want to know how likely it is that another meteorite will fall through your roof. In the real world it is unlikely because most houses are never hit by a meteorite and it takes a fluke for a meteorite to hit a particular house, even though it is possible for it to happen to any of them. As a result, most houses have zero meteorite hits, a few have one meteorite hit and very few or none have two meteorite hits. In Bayesian terms this is a good analogy of SETI in one possible scenario.

Yeah, I think that there is almost a 100% chance like genius said. I'm guessing around 98.6 and some other decimals percent chance.
Elroch, you make great points. As far as your point about communication to aliens, I am not saying we will find aliens but that there are aliens. And as far as your fluke point goes, I have two responses:
1) If our universe is infinite, there will be at least one other universe with aliens ad no fluke. This is just how probability goes.
2) If our universe is finite, than a fluke can happen through all universes and kill all alien life. This is highly unlikely, but not impossible. This, along with the possibility of our universe being small enough to not have any alien life, contributes to the small chance that there is no alien life.

Sure, my Bayesian Multiverse viewpoint implies the likelihood of aliens in other Universes, but it's an open question whether they are to be found in ours. Only time will tell.

I see no reason to believe that if the universe is infinite that there is a 100% chance that alien life exists (However, I share your conclusion that it almost certainly does). The premise that there are only a finite number of combination of things remains unproven (there may be finitely many building blocks, but it does not follow from this that there are finitely many combinations that result from finite elements). Given the truth of these 2 premises I also dont see how it follows that the universe must repeat itself (why is it logically necessary that there is just one finite region of combinations with the rest of the infinite universe just being empty?). Additionally, the claim that all possibilities must be cycled through given infinite attempts is not immediately true just as given an infinite sequence of even numbers one can never produce an odd number.
As an aside, it seems to me the reason why intelligent life is very likely in many universes is because that it is in the eventual interest of any intelligent life to prolong the lifespan of its universe, since the existence of such life depends on the lifespan of its universe. The longer a universe exists, the more time it has to do its job of imparting its laws wherever it can (reproducing). Cosmological darwinism is indeed inevitability at its finest. Alas I speculate.
Recently I've been arguing with some big christians about alien life. I believe there is alien life out there in our membrane(as i am sure most of you do). I am not saying there are for sure, just a very high probability. Heres why(in a nutshell):
Our universe(as in everything on our membrane) cannot have edges, so it can be two things: Finite or Infinite.A finite universe would be shaped like a torus, so that if you went in a straight line from point A, you would eventually arrive at point A again without making any turns. However, lights from stars and galaxies don't reappear in specific patters. This doesn't mean that the universe isn't finite. This just means that if it was, it would be very, very large, increasing the probability of there being aliens.
If our universe is infinite, than there is a 100% chance we will find aliens. This is for two things. One thing is that because the universe is infinite, but there are only a finite number of combinations of things, the universe must repeat itself, resulting in an identical earth. (FYI, This also eliminates parallel universes, as every possibility of life would be contained in our universe). The second thing is that there are combinations to make alien life, and if the universe is infinite, it will have to cycle through that(assuming that einstein is correct and the world behaves uniformly).
Sorry for the long post. Point out where I made mistakes.