You need to remember that “likelihood” is a technical term. The likelihood of $H$, $Pr(O|H)$, and the posterior probability of $H$, $Pr(H|O)$, are different quantities and they can have different values. The likelihood of $H$ is the probability that $H$ confers on $O$, not the probability that $O$ confers on $H$. Suppose you hear a noise coming from the attic of your house. You consider the hypothesis that there are gremlins up there bowling. The likelihood of this hypothesis is very high, since if there are gremlins bowling in the attic, there probably will be noise. But surely you don’t think that the noise makes it very probable that there are gremlins up there bowling. In this example, $Pr(O|H)$ is high and $Pr(H|O)$ is low. The gremlin hypothesis has a high likelihood (in the technical sense) but a low probability.

Source:

Sober, E. (2008). Evidence and Evolution: the Logic Behind the Science. Cambridge University Press.

As quoted in this answer to this question on CrossValidated.