Possibility is the condition or fact of being possible. The Latin origins of the word hint at ability. Possibility also refers to something that "could happen", that is not precluded by the facts, but usually not probable. Impossible denotes that something cannot happen or be done.
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we are not certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1, we call probability. The higher the probability of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the likeliness that a (random) event will occur.