Let $A$ and $B$ be two events in a sample space $\Omega$ such that $P(A) = 0.55$, $P(B) = 0.45$, and $P(A \cap B) = 0.20$. If an experiment yields a result in $(A \cup B)^c$, what is the probability that the result was in $A^c \cap B^c$?