Suppose we have a lone hollow metal sphere with net charge equal to $0$. If we were to put a point charge $Q$ inside of the sphere and move it, let's say, away from the sphere center at some distance $d$, determine the distribution of induced charge on the sphere. With no further explanation, the answer in my textbook states that the induced charge will be evenly distributed across inner surface of hollow sphere, no matter where the point charge is, as long as it is inside and not touching the sphere.
Can someone explain in detail or provide information on why this is true?