> "the" is used to mark noun phrases that are already present in the conversational context, and "a" is used to introduce new noun phrases into the conversational context.
> (Compare "there's some guy outside scaring customers away" with "there are some guys outside scaring customers away", then consider that a would only be permissible in the first one.)
This rule is OK but it fails for the following case: A man you've never seen before runs into your office and says "The President is outside!" Now, the President wasn't part of your conversational context, in fact there was no conversational context, nor any context with the speaker. But "a President is outside!" is clearly wrong.
More generally, any attempt to give simple rules for this part of English grammar will fail, and will not generalize to other languages with articles. The rules of natural languages are extraordinarily complex, although we have the illusion that we can understand them explicitly. That's why rule-based NLP systems have always seemed attractive, and have always failed.