Synonyms for Possibility (same or very similar meaning)
WordNet sense 1 (capability of existing or happening or being true):
possibleness
WordNet sense 2 (a tentative theory about the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena):
hypothesis, theory
WordNet sense 3 (a possible alternative):
opening, possible action
From the ODE community, based on WordNet
add/edit