I am not sure what you mean by "the form of the theorem looks much more arbitrary". The derivation of Bayes law comes from the axioms of conditional probability

I am not sure what you mean by "the form of the theorem looks much more arbitrary". The derivation of Bayes law comes from the axioms of conditional probability. Given two events A, B; we have: P(A^B) = P(A|B) * P(B) Probability of A and B = Probability of A given B happened times probability of B Symmetrically, we can say: P(A^B) = P(B|A) * P(A) Now we have: P(A|B) * P(B) = P(B|A) * P(A) Rearranging, we get: P(A|B) = P(B|A) * P(A) / P(B) So I do not see this as being particularly arbitrary. While other rational models are possible, I find this one rather practical and satisfying. [Edit]: markup