From a paper I am reading, I do not think the meanings of the parameters matters here but I can edit if that's useful to know.
$L(\phi, \theta \mid n, \omega) = Pr(n \mid \phi,\theta)Pr(\omega \mid n, \phi, \theta)$
So the likelihood has been factored into the product of the marginal of $n$ and the conditional distribution of $\omega$ given $n$.
I haven't had much formal stats training so I'm thinking there is some pretty standard knowledge that makes it obvious why you can do this but I don't know what to search for.
I've tried messing around with the chain rule and the definition of conditional probability $Pr(A | B) = Pr(A,B) / Pr(B)$ but I can't seem to make it work out. Can I do it just using these or is there something else I need to know about?