Observed electron distribution functions of the solar wind permanently exhibit three different components: a thermal core and a suprathermal halo, which are always present at all pitch angles, and a sharply magnetic field aligned strahl which is usually anti-sunward moving. Whereas Coulomb collisions can explain the relative isotropy of the core population, the origin of the halo population, and more specifically the origin of its sunward directed part, remains unknown. In this study we present the radial evolution of the electron velocity distribution functions in the fast solar wind between 0.3 and 1.5 AU. For this purpose we combine data measured separately by the Helios, Wind, and Ulysses spacecraft. We compute average distributions over distance and normalize them to 1 AU to remove the effects of the solar wind expansion. Then we model separately the core, halo, and strahl components to compute their relative number density or fraction of the total electron density. We observe that, while the core fractional density remains roughly constant with radial distance, the halo and strahl fractional densities vary in an opposite way. The relative number of halo electrons is increasing, while the relative number of strahl electrons is decreasing with distance. Therefore we provide, for the first time, strong evidences for a scenario that is commonly assumed: the heliospheric electron halo population consists partly of electrons that have been scattered out of the strahl.