Stabilizer of Element after Group Action

Theorem
Let $\struct {G, \circ}$ be a group.

Let $S$ be a set.

Let $*_S: G \times S \to S$ be a group actions.

Let $x \in S, a \in G$.

Then:
 * $\Stab {a * x} = a^{-1} \circ \Stab x \circ a$