What is probability? Changing the words of a phrase by it's synonyms may help to understand some concepts by approaching the speech to something more familiar to the audience, but that's not a definition at all, it's not adding information.
"A probability that an event P will have a result R is X if, when P takes place N times, on average, R will result X * N times" -> I don't know yet how to quote as fancy as you do, and would appreciate the help to learn!
But, life goes on: I don't know if you are saying that this is a definition, but assuming you are, it is just describing how to get to the magnitude of the probability of an event. It is like saying that price is the law of supply and demand.