What are the probabilities of our existence?
OK. There could have been many "existence" so the question should be asked "what is the probability of an existence that is 'interesting'" or something like that.
Technically, we cannot calculate, because we have no knowledge about the variety of processes that could have happen.
But we may try intuitively, with some understanding of the space of possibilities, to gauge. Where are the odds going to land?
In short, I see that it feels that the probability is very low. Not 1 / 1 ^ infinite zeros. But rather 1 / 1 ^ very many zeros.
Darwin killed 99.9999% of the improbability of existence.
But I believe, that while we may (and have to) intuit about these probabilities, we should learn from this experience is how far our estimates can be from the ultimate numbers.
Before Darwin, if asked what are the odds for this world, reply would be infinitely low. Because the probabilities for all these species and their complexity and efficiency is so impossible.
One good algorithm of Darwin (gradual process of evolutionary selection) dumped the probabilities infinitely. They still seem low, but in relation to the odds we had before Darwin, the odds are infinitely more probable.
Statistically, Darwin taught us how a not thought of process can change dramatically our subjective probability assessments.
We Know that our estimates are terribly unreliable. That is, after Darwin
Epistemologically, that is Darwin's most important lesson!