This.

Surprisingly enough, a human is much more likely to find oneself alive in a world in which humanity was not nearly made extinct by nuclear war.

Exponentially so, if we assume, reasonably, that even if humans survived (technically) a nuclear war, their descendants would take 100s of thousands of years or longer to recover to pre apocalypse levels, vs. non nuclear war realities where the population simply keeps increasing exponentially, leading exponentially many more humans to find themselves existing in that "timeline."