Let $A$ and $B$ be two events in a sample space. Define the symmetric difference $A \Delta B$ as the event that exactly one of the events $A$ or $B$ occurs. If $P(A) = 0.55$, $P(B) = 0.40$, and the probability that at least one of the events occurs is $0.75$, find the probability $P(A \Delta B)$.