While a three-dimensional (3D) scattering medium is from the outset opaque, such a medium sustains intriguing transport channels with near-unity transmission that are pursued for fundamental reasons and for applications in solid-state lighting, random lasers, solar cells, and biomedical optics. Here, we study the 3D spatially resolved distribution of the energy density of light in a 3D scattering medium upon the excitation of highly transmitting channels. The coupling into these channels is excited by spatially shaping the incident optical wavefronts to a focus on the back surface. To probe the local energy density, we excite isolated fluorescent nanospheres distributed inside the medium. From the spatial fluorescent intensity pattern we obtain the position of each nanosphere, while the total fluorescent intensity gauges the energy density. Our 3D spatially resolved measurements reveal that the differential fluorescent enhancement changes with depth, up to 26× at the back surface of the medium, and the enhancement reveals a strong peak versus transverse position. We successfully interpret our results with a newly developed 3D model without adjustable parameters that considers the time-reversed diffusion starting from a point source at the back surface.