Conditional Probability Under Sample Space Reduction

You have a set $B$ with $|B| = n$ elements, and a subset $A \subseteq B$ with $|A| = k$. You draw a uniformly random element from $B$. For any element $b \in B \setminus A$, what is the probability that $b$ was selected, given that the selected element is not in $A$? Derive the general formula, then evaluate it for $n = 10$, $k = 4$.