If two events are mutually exclusive, then the probability that they both occur is 0.

If two events are independent, then P(A B) = P(A) and vice versa. Thus, P(A and B) = P(A) * P(B).
P(A∣B)=P(A∩B)P(B)P(A|B) = \frac{P(A \cap B)}{P(B)}