Electromagnetic void space is a medium, while geometrically occupying a finite volume of space, optically equivalent to an infinitesimal point, in which electromagnetic waves do not experience any phase accumulation. Here, we report the first realization of three-dimensional (3D) electromagnetic void space by an all-dielectric photonic crystal possessing vanishing permittivity and permeability simultaneously. The 3D electromagnetic void space offers distinctive functionalities inaccessible to its 2D or acoustic counterparts because of the fundamental changes in topology, which comes from the ascension of dimensionality as well as the transverse nature of electromagnetic waves. In particular, we demonstrate, both theoretically and experimentally, that the transmission through such a 3D void space is unaffected by its inner boundaries, but highly sensitive to the outer boundaries. This enables many applications such as the impurity "antidoping" effect, outer-boundary-controlled switching, and 3D perfect wave steering. Our work paves a road toward 3D exotic optics of an optically infinitesimal point.