'Possibility' means the state of being possible - that it will happen. Usually, it refers to an all or nothing state. Either something is possible or it isn't. 'Probability' refers to 1) The state of being probable - not just possible, but that something is likely to happen. 2) The mathematical chances that something will happen. "The probability of rain tomorrow is 50%." You would not hear about the possibility being 50%. The biggest difference - 'probability' can be quantifiable, 'possibility' cannot.