Not how it works, Bali, and you're only proving my point. There doesn't have to be a law that gives an employer permission to fire an employee for anything; an action is considered legal unless a specific law makes it illegal.
So. Where's the law that makes firing an employee for suspicion of drinking on the job illegal? Hurry up, Bali, the OP is waiting for you to rescue her from the misinformation the rest of us are feeding her. If you don't post a link to that law, she might believe we're right.
Oh, that's right. There is no such law and we are right. How about that?