More than the probability of some event we need to know the frequency with which potential conditions for it are repeated.
To illustrate: Imagine you have a mysterious caller one day who invites you to take part in an 'experiment'. There's a cash prize if you're successful so you agree to go along. You're asked to take a coin from your pocket and toss it ten times - the experimenter tells you that you will obtain ten heads in a row.
You doubt this very much because you have some understanding of the unlikelyhood of that outcome but you give it your best shot. You toss your coin and get ten heads!
What would you think of that?
For something to exist there needs only to be the probabilistic possibility that it can exist.
In the absence of any clear idea of what the underlying initial conditions were from which our Universe emerged, how can we hope to draw any conclusions about how unlikely this particular composition of the Cosmos is?
What we can be very confident about is that what followed the Big Bang appears to have been entirely naturalistic.
In order to draw a possibility one needs to know what the possibilities are, meaning what could have gone right or wrong, the odds!?