I'd say that luck is how we choose to recognize the effects of probability. "Good luck" is the conscious recognition of probability outcomes that have positive effects on us, or the attribution of such outcomes to probability alone (regardless of whether that's correct -- how many people do you know who try to shrug off compliments, or claim helplessness, by invoking luck). "Bad luck" is the same regarding negative effects. If we ignore the role of probability, or misattribute its role to something different, we don't recognize any luck at all.
Of course, if we were all omniscient, there wouldn't be nearly as much room for the idea of luck -- but we're not, we don't know all the events that lead up to all the things that happen in our lives. But we do often know the general odds of something happening or not happening, and we can label happenings as "luck."
Example 1: you could say it was "good luck" that caused you to be accepted into a very selective college. It's certainly possible that an admissions officer used a random number generator to select your application and admit you, but it's more likely that the person read your application (the product of your personal efforts), judged it to be worthy, and recommended you for acceptance. Whatever happened, you have no way of knowing exactly what it was, so you can choose to call it "good luck" if you wish.
Example 2: You have exercised, eaten healthily, and lived in a clean environment all your life. Now you have cancer. The doctors can't tell you what caused it (something you did, something you didn't do, some genetic predisposition that would have screwed you over no matter what, magic, voodoo, ancient curse, whatever). Because you have no information on how it happened, the only descriptive explanation you have left (insufficient as it may be) is "bad luck."
(Not at all presenting this as a complete theory, just throwing it all out there.)
