$\dfrac{p(Y,Z)}{p(X,Y,Z)}$ = $\dfrac{p(Z|Y)p(Y)}{p(X|Z,Y) p(Z|Y) p(Y)}$ = $\dfrac{1}{p(X|Z,Y)}$
If it changes anything, P(Y,Z) and P(X,Y,Z) are intractable.
2026-05-04 08:52:20.1777884740
Is this probability equation involving 3 variables correct?
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Yes. You can do it in one step. $\frac{p(X,Y,Z)}{p(Y,Z)}=p(X|Y,Z)$ so taking the reciprocal of both sides we get the desired result.