The Blind Contestant Knows His Cap

A game-show host displays $5$ caps — $3$ green and $2$ orange — to three contestants, then dims the lights, places one cap on each head, and hides the two leftover caps. Lights up: each contestant can see the others' caps but not his own. Contestant one, fully sighted, admits he cannot deduce his cap color. Contestant two, also sighted and having heard him, then admits the same. Contestant three is blind — yet he immediately and correctly announces his cap color. What is it, and how does he reason?