ability = skill possibility = chance, opportunity

ability-умение.possibility-возможность

Ability means 1.The quality of being able to perform; a quality that permits or facilitates achievement or accomplishment 2Possession of the qualities (especially mental qualities) required to do something or get something done. whiles possibility 1.A future prospect or potential "this room has great possibilities" 2.Capability of existing or happening or being true "there is a possibility that his sense of smell has been impaired" 3.A tentative insight into the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena 4. possible alternative "bankruptcy is always a possibility" cowboy...

they aren't even synonyms :P

But wait, you think they have a lot in common or similar?