  Ayer went on in later work to examine the problem of induction in greater detail, in particular in relation to attempts to make the problem tractable by appeal to notions of probability. In 1957 he wrote an important article attacking the idea that the logical conception of probability could be a useful guide to the future. Given a proposition, a, that a horse is going to win the race, and various sources of evidence, h1, h2, h3…hn, one can estimate the probability of a given h1 to be p1, given h2 to be p2, and so on. One can also estimate the probability of a given all of h1 …hn. Call this probability pn, it being the probability of a given all of the evidence available to the person wishing to place a bet on the horse. Which of these probabilities, asks Ayer, would it be rational for this person to base their bets on? Common sense dictates that pn is the best estimate, but Ayer argues that on the logical conception of probability, all of the estimates p1…pn are logically true, and so it is impossible to single out one as being ‘better’ than any of the others.