It also, to me, implies a possible prior confrontation between the two people. If a stranger is where he doesn't belong, you would probably say somethings like "What are you doing here?" or "This is restricted property" or something like that. After all, if he's a stranger, you don't know what his "business" (in this context, purpose/motive/intent) is, and whether it actually does make sense for him to be there.