I know maximum likelihood and Bayes formula works for both frequentist and Bayesian approach. We know there are two approaches to statistics, and likelihood is a term that is used in both frequentest and Bayesian approach.
I heard that for Bayesian case likelihood in general case will not add to 1 and you may check and see the Wikipedia has a formula without using $\mathbb P$ for likelihood:
$$ \mathbb{P}\left(\theta \mid x_{1}, x_{2}, \ldots, x_{n}\right)=\frac{f\left(x_{1}, x_{2}, \ldots, x_{n} \mid \theta\right) \mathbb{P}(\theta)}{\mathbb{P}\left(x_{1}, x_{2}, \ldots, x_{n}\right)} $$
Is still the case the likelihood will not add to 1 in frequentist case as well? I checked the post on difference but unless I haven't understood something I haven't found the answer to my question.
To me simplified likelihood is something that we already measured, and probability is something that hasn't happened yet.
