There is another angle through which you could attempt to determine the probability of you existing. It's by dividing number of people on Earth today, by total number of genetic permutations possible. Of course that would remove cultural factors from the equation... but calculating actual probability of cultural factors are pretty damn hard!
The total number of bases in human DNA is ~3E9, so there are 4^3E9 ~= 10^2E9 possibilities. But this number includes a huge kind of variations, from humans to cows, to whales, to bats, to cats, to algae, to fungus, to pines, to orange trees, to roses, to petunias, to artichokes and probably even to vulcans, and to unicorns :).
(Different species have different number of bases in their DNA, but all the eukaryotic cells have the same order of magnitude, so we will just ignore this fact.)
If we consider only single nucleotide polymorphisms, the difference between two humans is in only 1/1000 of the bases (and let’s suppose that in each case the difference is in the same bases, and that the variations are independent) . So with this restriction there are 4^(3E9/1000)~=10^2E6 "possible" humans. Using that the total number of people that have ever lived is estimated as 10^11, the probability is 10^11/10^2E6 ~= 1/10^2E6.
But, please, don’t take these numbers very seriously.
But identical twins have the same genes, so even if your gene sequence came into existence, it doesn't mean that you would exist (whatever that means). Sentience is weird.
