Starting off in prison seems to be a bit of an Elder Scrolls tradition. I mean, in Arena, as I understand it, you started in prison, in Morrowind, you didn't begin in prison, but that's because you begin when you're just getting off the boat that brought you to Morrowind to be released, and yes, you're being released from prison. In Oblivion, you start the game in prison and get the chance to escape when the Emperor is escorted by the Blades along an escape route that happens to pass through your cell. I'm seeing a clear trend here, the only game that really seems to break it is Daggerfall, which has you starting in a dungeon, and that's certainly closer to starting off as a prisoner than starting off on a farm or something, seeing as it still involves you being trapped in an unpleasant place and needing to get out. If anything, in terms of the actual impact on gameplay, Morrowind breaks the tradition more than Daggerfall because you never had to fight your way through a dungeon to reach freedom, you just needed to walk off the boat, talk to people, fill out forms, and then the game dropped you in the middle of a town. And I wouldn't be surprised if Skyrim keeps the tradition, but obviously, we can't be sure until Bethesda tells us how the game will start.
I'd say that aside from being a matter of tradition. I'd say beginning the game as a prisoner has a few advantages, first, it allows you to start off with nothing, as your possessions would have been taken away from you when you when you were arrested, and the fact that your skills are low might have been caused by your forgetting some things while in prison due to having gone for a long time without using them, kind of like the mechanic that's already in the games when you do time. Plus, as long as the game doesn't explain why you're in prison or what you did before getting arrested, it really doesn't force a specific background on the player. Some would argue, of course, that it indicates that your player must have been a criminal, but I don't think that's necessarily the case. Sure, maybe the player is in prison for something like theft or murder, but at least in Morrowind and Oblivion, it was really left up to your imagination. Maybe the whole thing was just a misunderstanding, maybe you got framed by someone, or maybe you got a little too drunk and did something you would later regret once you were sober again, assuming you remembered it, or maybe you were just trying to be polite and pick up the strawberry you knocked on the floor. It's really up to you to decide. Now if your character started off as say... a mercenary, it would raise the question as to why you don't at least have basic equipment, and would seem to force some at least minor background on your character. And the best introduction to an Elder Scrolls game, I would say, would succeed in forcing as little backstory upon the player as possible.
You're a prisoner of war (that way you needn't worry about an ambiguous criminal backstory) being held in a fortress or something in the midst of an assumed civil war or at least a minor siege. The guards, falling back, release you with the opportunity to help repel the invaders to win your freedom. That, or they're outright killed in front of your cell and you just loot the key.
From there, you can either familiarize yourself with the game by fighting through a tutorial area, or you can just make a mad dash for the exit and be done with it. Something along those lines.
That might actually not be a bad idea, depending on where the story goes. Part of what I like about it is that it allows the player the oportunity to skip the tutortial, not like in Oblivion where you had no choice but to go through the prison and sewers.