It's not an idiom, just impossible to translate literally in English. Reason has a meaning in Latin languages to express you have a rational explanation/reason behind. It's a way to say that the explanation given makes sense, has a logic.
Notice that in British English Maybe you have reason is a valid sentence borrowed from Latin in a literal fashion. Reason in Latin is tied with Logic, this sentence basically means Maybe what you say has a logic
ElakVarg, I'd be splitting hairs if I said there's a difference. In most cases they'd be used interchangeably. The subtle difference is that something that will 'probably' occur is more liable or likely to occur than if 'maybe' were used. So: "Maybe you're right" = e.g. 50% chance of you being right; "Probably you're right" = e.g. 75% chance you're right. That's I believe the difference. Think of how weather forecasters' predictions: "Maybe it'll rain tomorrow" vs "Probably it'll rain tomorrow" I'd personally be more likely to take an umbrella with me in the latter case, then the former.