In this work, we propose and experimentally demonstrate an entropy loading technique based on probabilistic constellation shaping for a visible light communication (VLC) system. The aggregated achievable bit rate of a multi-carrier signal is maximized, considering a given pre-estimated signal-to-noise ratio. A study of the ideal number of subcarriers and signal bandwidth was performed using multiplexed red, green and blue lasers diodes with a bandwidth of 1 GHz. With a 20 degree optical diffuser, the communication system is able to cover a wide area at a free-space distance of 0.90 m, while achieving a record aggregate bit rate of 31.2 Gbit/s for single-polarization RGB-VLC systems.