My intuition is that, if $A$ is $\mathcal{G}-$measurable, by definition, $A \in \mathcal{G}$, which means event $A$ is an element of the collection $\mathcal{G}$. There must be an event $G \in \mathcal{G}$ happened because of the given condition, which leads to two possible situations: either $G$ is $A$ or not (hence $P(A | \mathcal{G}) \in \left\{0, 1\right\}$), since we excluded all the uncertainty.
Is my understanding correct?