Another example of a very small probability that is not zero is the probability of winning against a much better chess player. Say one of us against the latest Stockfish.
This can be intuitively seen to be true by considering a deeper evaluation of the moves played by the two players and observing that there is a finite probability on two consecutive half moves that the weaker player plays a better move than the stronger player. With a reasonable assumption about some degree of independence, this means there is a finite probability of this happening on enough consecutive moves to achieve the victory.
The finite probability involved for this extreme reverse domination is so absurdly small as to be safe to believe it would not happen in practice, but no-one with an understanding of probability could seriously deny it is not a strictly positive probability. (It is of course not the only way a win could be secured, but emulates a typical theme of mathematical proofs of finding an easy route to the conclusion rather than dealing with all the inessential details).


I believe it happens to some people, when they're completely intent on winning a point, where there's no point they can logically win. So they make fools of themselves, but I'm sure that can't be you and I've misunderstood.