Show that the postulates of probability are satisfied by conditional probabilities. In other words, show that if

Question:

Show that the postulates of probability are satisfied by conditional probabilities. In other words, show that if P(B) ≠ 0, then
(a) P(A| B) ≥ 0;
(b) P(B| B) = 1;
(c) P(A1 ∪ A2 .. ∪ . | B) = P(A1| B) + P(A2| B) + · · · for Any sequence of mutually exclusive events A1, A2, ∪ . ..