This paper presents a channel-adaptive probabilistic shaping (CA-PS) scheme for 3D-24QAM signals, utilizing a hierarchical nested geometric structure to transmit training sequences. It computes the BER of each constellation point and adjusts transmission probabilities dynamically using Huffman coding, prioritizing points with lower BER. We achieved 51.59 Gb/s transmission over a 2 km, 7-core optical fiber system. At a HD-FEC threshold of 3.8×10^-3, the scheme demonstrated a received optical power of -13.0 dBm, yielding a sensitivity gain of 1.2 dB over conventional 3D-24QAM signals, and a 0.6 dB gain over Maxwell-Boltzmann distribution-based probability shaping with the same constellation geometry.