I find it helpful to think about probabilities as I think about inequalities. If we say that x>7, then we are making an uncertain claim about the possible values of x, but we have no idea what value x actually has. However, from this uncertain claim about the value of x, we can make the true claim that x≠5.
Similarly, when we prove that a probability is nonzero, it means that whatever it is we are talking about must be true somewhere within possibility space.
I find it helpful to think about probabilities as I think about inequalities. If we say that x>7, then we are making an uncertain claim about the possible values of x, but we have no idea what value x actually has. However, from this uncertain claim about the value of x, we can make the true claim that x≠5.
Similarly, when we prove that a probability is nonzero, it means that whatever it is we are talking about must be true somewhere within possibility space.