In this Letter, we provide a novel maximum a posteriori probability detection-based decision-directed carrier phase estimation (MAP-DDCPE) algorithm. The introduced probability-aware maximum a posteriori probability (MAP) detection avoids the decision errors brought by an ununiform probability distribution, which enhances the phase-tracking ability for the probabilistic shaping (PS) signals. With the proposed MAP-DDCPE, we experimentally demonstrate the 96-channel transmission that delivers 40-GBaud polarization division multiplexing (PDM) PS-64-ary quadrature amplitude modulation (64QAM) signals over the 2-km nested anti-resonant nodeless fiber (NANF). We believe the PS-assisted broadband NANF transmission enabled by the MAP-DDCPE is a promising solution for large-capacity optical communication.