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The question is a confusion of *probability* with *odds*.

*Probability* and *odds* can both be expressed as ratios with the same numerator but different denominators: speaking loosely, the probability of an event $X$ is the ratio of the number of cases in which $X$ occurs to the number of cases in which either $X$ or $¬X$ occurs; and the odds of $X$ is the ratio of the number of cases in which $X$ occurs to the number of cases in which either $X$ or $¬X$ occurs.

In doing calculations (like this one) using Bayes' Law it can be easy to confuse the two, because "updating the probability we accord to our hypothesis $H$ given evidence $E$" is equivalent to "multiplying the odds $\frac{P(H)}{P(¬H)}$ we accord $H$ by the likelihood ratio $\frac{P(H|E)}{P(¬H|E)}$ given us by the evidence."

In other words, I expect it's (relatively) easy to confuse odds with probability in certain Bayesian inference problems, because the formulation of Bayes' Law in terms of odds is much simpler in the case of binary hypotheses.