 Consider the first horse listed in the race, Athena. There are two possibilities, that she will win and that she will lose. Our evidence (or lack thereof) favors neither possibility, so the PoI says the probability that she’ll win is \(1/2\). But suppose there are three horses in the race: Athena, Beatrice, and Cecil. Since our evidence favors none of them over any other, the PoI requires that we assign probability \(1/3\) to each, which contradicts our earlier conclusion that Athena’s probability of winning is \(1/2\).