Al Gore defies the laws of probability

As if the huge success of An Inconvenient Truth followed by winning the Nobel Peace Prize wasn't enough, now Al Gore is defying the laws of probability! At least in terms of probable outcomes of the U.S. Democratic nomination and the presidential election itself.

Intrade, the leading commercial prediction market lets you bet on political outcomes. For example, "Barack Obama to win 2008 US Presidential Election" is currently trading at 47.5, meaning the market believes there's a 47.5% chance Obama will be the next president.

What's the probability that Al Gore will win the Democratic nomination? As I write this, the market believes it's 1.7%. Seems fair enough ...

... until you look at the probability that Al Gore will be the next president. Curiously, the market believes that's 2.1%. How could that be? Don't you have to win the nomination before you have a chance of becoming the president? (My 13-year-old daughter points out that perhaps Gore could run as an independent, but hey, we're Canadians, so this is a great mystery to us. So for now, let's leave this possibility aside.)

Let's do a few probability calculations (note that the vertical bar | means "given than"):

Prob(Gore pres.)
= Prob(Gore pres. & Gore nom.)
= Prob(Gore pres. | Gore nom.) * Prob(Gore nom.)

Therefore

Prob(Gore pres. | Gore nom.)
= Prob(Gore pres.) / Prob(Gore nom.)

So

Prob(Gore pres. | Gore nom.)
= 2.1%/1.7% = 123.5%

Therefore, if Gore is nominated, the probability he'll be elected president is 123.5%!

Of course there's no such thing as a probability above 100%, which suggests that something is amiss. Perhaps there is a belief that Gore might run as an independent, which would invalidate my assumption that he would have to win the Democratic nomination in order to become president. Or perhaps at any given time the prediction market isn't strictly coherent in the Bayesian sense that it should be consistent with the axioms of probability.

My interpretation is that Gore remains sufficiently attractive as a presidential candidate that if he were nominated, the chances of him winning the election are very high. But not quite 124%.