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 literally cannot happen or be done.
Probability, or chance, is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
Plausible deniability is, at root, credible (plausible) ability to deny a fact or allegation, or to deny previous knowledge of a fact. The term most often refers to the denial of blame in (formal or informal) chains of command, where upper rungs quarantine the blame to the lower rungs, and the lower rungs are often inaccessible, meaning confirming responsibility for the action is nearly impossible. In the case that illegal or otherwise disreputable and unpopular activities become public, high-ranking officials may deny any awareness of such act or any connection to the agents used to carry out such acts. It typically implies forethought, such as intentionally setting up the conditions to plausibly avoid responsibility for one’s (future) actions or knowledge.