@rahul
when A and B are independent events
(1)Intuitive way: When A and B are independent, if A happens or does not happen it should not affect B, similarly if B happens or does not happens, it should not affect A.
so P(A|B)=A and P(B|A)=B.
(2)Proof :
When A and B are independent events, they can occur together and probability of them occurring together is
P(A$\cap$B) = P(A).P(B)
and Since, $P(A|B) = \frac{P(A\cap B)}{P(B)}$
So, P(A|B)= P(A).
Similarly goes for P(B|A)=B.
Yes, but when A and B are mutually exclusive, then it means that A and B are dependent.
When A occurs, it rules out the probability of occurrence of B, and When B occurs it rules out the probability of occurrence of A.