I was reading that $\sum_{z \in Z}O(a, s',z) =1$, with:

$a$ = action

$s'$= next possible state

$z$ = a certain/specific observation

How come that the observation function $O(a, s', z)$ adds up to $1$ in POMDP?

To me it is like there is always a way to capture a state in POMDP. But it should be not since the states are only partially observable.

Source: https://www.sciencedirect.com/science/article/abs/pii/S0022249609000042 p.120