In some sense, the definition of probability is spread out among the whole chapter until the word is first used; as far as I can tell, the definition of probability he gives is "the unique real associated with a hypothesis where the product and negation rules can be applied without an additional transformation, and without breaking consistency with the desiderata."

I was actually thinking about how to give a concise and intuitive version of the Bayesian definition of probability earlier today, and find this very disconcerting. It would feel awfully wrong to echo everything bad I've heard about frequentism while relying on the measure theoretic definition of probability for intuition.