Inclusion-exclusion formula example

Question

Compute the probability that a hand of 13 cards contains ace and king of at least one suit.

I cannot understand why we use hear inclusion-exclusion formula. For the "at least" problems the common solution is $1 - P(A)$.

So the questions are:

1. Why do we use inclusion-exclusion formula in this case?
2. In general when should we use this formula

Thank you