1. possibility; chance; likelihood; probability
おそれ is often preferred for negative outcomes
なぜこの可能性を考えなかったのだろう。Why didn't I consider this possibility?
2. potential; potentiality; promise
そう、それは無限の可能性を感じさせるものだった。Yes, it was something that made one feel infinite potential.
3. possibility (modal property of a proposition containing no logical contradiction)