As we’ve discussed before in other contexts, one can divide two probabilities like these to obtain a conditional probability: e.g., if the Democrats put X on the ticket, they will win the general election Y% of the time (where Y = odds of X becoming VP/odds of X being nominated).

These markets are thin, so the conditional probabilities should be taken with a grain of salt. But they are interesting nonetheless:

The pattern I see here is that conditional probabilities are higher for fresh faces (Webb, Sebelius; and arguably Bayh and Richardson despite their longer tenure) than for the old guard (Clinton, Nunn, Biden).

Of course, these should be viewed as correlations, not necessarily causal effects. For example, two possible explanations are: 1) putting a fresh face on the ticket helps Obama, either because there is less baggage or less of a contrast in national-politics resume length, or 2) Obama will only pick an old guard candidate in the state of the world in which he needs to shore up a weakness (i.e., picking Clinton to end a civil war, or Nunn to add foreign policy experience).
On the GOP side:

Huckabee has the highest conditional probability, and Pawlenty and Jindal are noticeably lower. Interpreting this one is harder: it depends on what aspect of Huckabee one thinks the market is expecting to be appealing (religion, likeability, Southernness, selective economic populism).

Technical note: the bids and asks reported above are actual quotes scrapped this AM; the mids are (bid+ask)/2, rescaled to add to 100 across all candidates.