(きかい) A chance, as in, “I hope I will have a chance to go to Australia someday.” Or, “This could be my only chance to see yo mama’s huge collection of Rosie O’donnel pap-smears.”
きっかけ A chance or opportunity. Unlike the related word 機会、きっかけ is used with opportunities that one DID take. Usually used in the phrase きっかけをつかむ (to seize the opportunity).
(かのう) A possibility. xxx可能性がある=”there is a possibility of xxx.”