> https://en.m.wikipedia.org/wiki/The_Unreasonable_Effectivene...
> It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them.
This seems like a well written but misleadingly titled article. The title implies the article will make an argument about the philosophy of statistics, but the article is basically just saying "conditional probabilities are useful" without further speculation as to why they're so useful. As parent comment suggested, a likely reason for its effectiveness is that this is applied mathematics so we should not think it unreasonable that conditional probability is effective.
They are not unreasonable effective.
It's just that sampling from probability distributions is computationally expensive, which has lead to the development of frequentist statistics (as opposed to Bayesian statistics). Frequentist statistics is unreasonably effective, since it makes so many assumptions that its hard to do a frequentist statistical analysis without violating some of the assumptions the methods have with regards to the data distributions, etc.