Wiki gives this example to illustrate likelihood.
Imagine flipping a fair coin twice, and observing the following data: two heads in two tosses ("HH"). Assuming that each successive coin flip is i.i.d., then the probability of observing HH is
${\displaystyle P({\text{HH}}\mid p_{\text{H}}=0.5)=0.5^{2}=0.25.}$
given the observed data HH, the likelihood that the model parameter $p_\text{H}$ equals 0.5 is 0.25. Mathematically, this is written as
${\displaystyle {\mathcal {L}}(p_{\text{H}}=0.5\mid {\text{HH}})=0.25.}$
This is not the same as saying that the probability that $p_\text{H} = 0.5$, given the observation HH, is 0.25. (For that, we could apply Bayes' theorem ...)
Assuming that probability is 0.25, How to exactly apply Bayes' theorem on that? in opposed to "the likelihood is 0.25"?