possibility has 5 distinct synonyms spread across 3 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is impossibility.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a future prospect or potential
“this room has great possibilities”
capability of existing or happening or being true
“there is a possibility that his sense of smell has been impaired”
Synonyms, antonyms and the broader and narrower relations for possibility come from Princeton University’s WordNet. Full sources and licences.
a tentative insight into the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena
“a scientific hypothesis that survives experimental testing becomes a scientific theory”