Question

best of bayes theorem

Answer 1

You don't need a book for Bayes' theorem. It tells you how to find one conditional probability in terms of the inverse conditional probability. Here it is.  

Let E and F be events.  Then

                                   P(E|F)=P(F|E)P(E)P(F)P(E|F)=P(F|E)P(E)P(F)

Here's a proof of it.  By definition,

                                   P(E|F)=P(E∩F)P(F).P(E|F)=P(E∩F)P(F).  

But P(E∩F)=P(F|E)P(E)P(E∩F)=P(F|E)P(E) since P(F|E)=P(E∩F)P(E).P(F|E)=P(E∩F)P(E).   Q.E.D.

You'll find Bayes' theorem in any book about probability soon after where conditional probability is introduced.