The limited modulation bandwidth of the light emitting diodes (LEDs) presents a challenge in the development of practical high-data-rate visible light communication (VLC) systems. In this paper, a novel adaptive coded probabilistic shaping (PS)-based nonorthogonal multiple access (NOMA) scheme is proposed to improve spectral efficiency (SE) of VLC systems in multiuser uplink communication scenarios. The proposed scheme adapts its rate to the optical signal-to-noise ratio (OSNR) by utilizing non-uniformly distributed discrete constellation symbols and low complexity channel encoder. Furthermore, an alternate optimization algorithm is proposed to determine the optimal channel coding rate, constellation spacing, and probability mass function (PMF) of each user. The extensive numerical results show that the proposed PS-based NOMA scheme closely approaches the capacity of NOMA with fine granularity. Presented results demonstrate the effectiveness of our scheme in improving the SE of VLC systems in multiuser scenarios. For instance, our scheme exhibits substantial SE gains over existing schemes, namely, the pairwise coded modulation (PCM), geometric shaping (GS), and uniform-distribution schemes. These findings highlight the potential of our approach to significantly enhance VLC systems.