Based on their separate and mutual records, what chance does Karjakin have against Carlsen? I was slightly disappointed with the recent result at the Candidates.

Karjakin won, but I just don't think he can match Carlsen for the WCh title.

What is the most accurate prediction of the probability of Karjakin being victorious over Carlsen this November? (I.e. the prediction that takes the most relevant data into consideration.)
One of the Russians (Filatov?, maybe even Karjakin himself?) brown-nosed to the media that every match is 50-50 odds on the face of it...

But more seriously, Carlsen's rating has consistently been 2850 plus/minus a small amount (20) for some time now, while Karjakin has been more volatile, currently 2775 (near his career best 2788 of July 2011). So I think a 75 Elo advantage in raw strength must be assumed from the outset. This is about 60% scoring per game, and if this were the only factor, then over 12 games then Carlsen should win 7.25 to 4.75 or so, or likely 3-1 with 8 draws. Mathematically, one can model it one way or another (Poisson process), and get that if Carlsen is 30% wins, 8% losses, 62% draws in any game (ignoring color as a first approximation), then he has a 86% chance of winning in regulation, 6% of losing in regulation, and 8% chance of reaching a tiebreak. So nominally a bit over 90% for Carlsen, by Elo.

OK, that's the pure stats version (like Chess by the Numbers might give). What sort of "corrections" to raw Elo might one give here? First there is the "hunger" factor, which I tend to discount. Second there is the preparation work of each (and their armies of helpers), where Karjakin might have a slight edge. But even if Karjakin wins one full game by prep (rather unlikely, at best he probably gets a superior position in two or three games, with a lot of work still to do), Carlsen still has about a 75% chance of winning by the above Elo estimation.

Finally there is the "grappling" aspect, whether the strength of one player matches up against the weakness of the other, or vice-versa. This is where the chess knowledge of their styles and past meetings would come into play. Karjakin seems assured that his Queen's Indian Defense against d4 can hold as Black, and I'd expect him to play the Berlin against e4. On the other hand, Carlsen has shown himself quite happy to play Nf3 systems (including early g3), just to divert from theory, so I can't think this means much. 

As for later in the game, I would say that Karjakin's technical capacity (endings, maybe also material imbalances), both in conversion and defense, is probably slightly superior to Carlsen's, maybe simply because the latter is never pushed so hard in this direction. But Carlsen has the clear edge in semi-dynamic positions (think Fischer), and I don't think Karjakin can hope to avoid these for 12 games (including 6 Blacks).  Finally, both seem to play "messy" positions reasonably well, though perhaps not like a specialist might (Morozevich, just to name a name).

But this might be Karjakin's best meta-plan, to aim for chaos game-after-game, hoping that Carlsen cracks, and/or starts to doubt himself. Unfortunately, Karjakin's style is more typically "small-ball", where he nibbles away with a small edge, first ensuring two results (especially on the Russian team, they would give him White on Board 2 or 3 against a 2650-2700, and expect him to grind out a win this way), and then slowly applying pressure for a victory. I don't see this as particularly that effective against Carlsen (or some other 2800ish players for that matter). On the other hand, Karjakin has previously shown himself to be adaptable in style to suit occasions, and if he objectively looks at the Elo calculation of above, might very well decide to play a bit out of character.

This is all to say nothing of the media circus and other side events that can cause disturbance to the players. Carlsen didn't face the "Russian full-court psychology" when playing Anand, but in the end I don't think it will affect him much.