In: Statistics and Probability
The probability is exactly equal to 0 means the event never happen any more. For example if we say that the chance of being involve in road accident is 0, it means that accident will never happen and you will be safe.
In the probability theory, the probability of certain event is 0 means it's impossible event at all. The event dosen't happen any way. We can take one more another example, suppose that we throw the dice which have only two faces with numbers 0 and 1. It means that sample space contain only 2 elements 0 and 1. If we ask that, what is the probability that we get 2 when we throw this particular dice, it's 0. We can't get 2 anymore because there are only 2 possibilities 0 or 1.
Hence in probability, the probability equals to zero means certain event never happened.