OK, so i cannot understand how to derive relationship between unconditional and conditional PMF, given an Event A, with P(A) > 0.
I know that $p_X(x) = P(A) \times p_{X|A}(x)$, but from definition of conditional probability, $p_{X|A}(x) = \frac{P(X=x\cap A)}{P(A)}$
Also by definition $p_X(x) = P(X=x)$. Combining these I get that $P(X=x) = {P(X=x\cap A)}$. Where am I going wrong?