The problem is that the universe is finite (15 billions years?) - you do not have infinite time for all special cases. Some "special cases" cannot possibly occur even within the timeframe of the age of the universe, e.g. the self-assembly of a protein molecule for example.
LOL, so that's where you were going with that.
I wasn't going in that direction, myself. Since you bring it up, however, I'll point out that much larger molecules than proteins self-assemble on a very short timescale, so you might want to re-think how you calculate those probabilities. The science of doing that is called chemistry.