The Adams Thesis for a conditional → says that P(A→B)=P(B|A). There are lots of theorems, most notably due to Lewis, that say that this can't be right, but they all make additional assumptions. On the other hand, van Fraassen has a paper arguing that any countable probability space can be embedded in a probability space that has a conditional → which satisfies the Adams Thesis and a whole bunch of axioms of conditional logic. The proof in the paper appears incomplete to me (it is not shown that all necessary conditions for the choice of [A,B] are met). Anyway, over the last couple of days I've been working on this, and I think I have a proof (written, but needing proofreading) of a generalization of van Fraassen's thesis that drops the countability assumptions (but uses the Axiom of Choice).
The conditional logic one can have along with the Adams Thesis is surprisingly strong. In my construction, for each A, the function CA(B)=(A→B) is a boolean algebra homomorphism. Thus, we have Weakening, Conjunction of Consequents, Would=Might, and the Conditional Law of Excluded Middle. The main plausible axioms that we don't get are Weak Transitivity and Disjunction of Antecedents (can't get in the former case; don't know about the latter).
The proof isn't that hard once one sees just how to do it, but it ends up using the Maharam Classification Theorem, the von Neumann-Maharam Lifting Theorem and oodles of Choice, so it's not elementary.