I have encountered an expression in my studies and am trying to determine if it correctly represents the conditional probability ($ P_{Z|X}(z|x) $). The expression is as follows:
$$ \sum_{s \in S} P_S(s) P_{Z|S,X}(z|s,x) $$
In this expression, ($ P_S(s) $) seems to denote the probability of ( s ) in set ( S ), and ($ P_{Z|S,X}(z|s,x) $) is the conditional probability of ($ Z $) given ($ S $) and ($ X $).
My question is: Does the above summation indeed yield ($ P_{Z|X}(z|x) $), and under which conditions or assumptions would this be accurate?
Any insight or guidance on this matter would be greatly appreciated.
Thank you for your time and help!