What is the probability of an event that is impossible? suppose that a probability is approximated to be zero based on empirical results. does this mean that the event is impossible?

If an event is impossible, the probability of it occurring is 0.

If empirical results approximate the probability to be zero, that does not imply the event is impossible. This is because empirical results are based on what has happened before. But any event that ever occurred had a first occurrence, and before that it had never occurred, which would have made its empirical probability 0.

Basically, there's a first time for everything, unless it actually is impossible.