Given enough time, even with a random process you will have iterated through every possible result some day. So inevitable here means, it would have to happen at some point, simply because it is possible. So, math.
That highly probable events actually happen can be a reasonable practical assumption, but definitely not a logical certainty.
It is the hard, probabilistic version of the sorites paradox: with few atoms and little time, any chemical process is unlikely; with a whole planet and a few billion years, chemical processes are very likely; at some intermediate sample size you can feel justified to assume that what you are interested in happens, but it is only a feeling, not a real qualitative threshold.