The (“Bayesian”) framework explored in these essays replaces the two Cartesian options, affirmation and denial, by a continuum of judgmental probabilities in the interval from 0 to 1, endpoints included, or—what comes to the same thing—a continuum of judgmental odds in the interval from 0 to infinity, endpoints included. Zero and 1 are probabilities no less than 1⁄2 and 99⁄100 are. Probability 1 corresponds to infinite odds, 1:0. That’s a reason for thinking in terms of odds: to remember how momentous it may be to assign probability 1 to a hypothesis.”
Richard Jeffrey, “Probability and the art of judgement”.
I leave it as an exercise to correctly state the relationships between Eliezer’s article, the Jeffrey quote, and the value of P(A|A).
(Note: Jeffrey is not to be confused with Jeffreys, although both were Bayesian probability theorists.)