We investigate the rate adaptability of quadrature amplitude modulation (QAM)-based probabilistic constellation shaping (PCS) using a fixed forward error correction (FEC) scheme over a wide range of information rates (IRs). Blind adaptive equalization that does not sacrifice any of the IRs was adopted. We show that the conventional decision directed least mean square (DDLMS) algorithm can cause a problem of mis-convergence when it is applied to the PCS of a low IR. To avoid the mis-convergence of DDLMS, we propose a DDLMS-based algorithm that simultaneously minimizes the error between the average symbol power of filter outputs and that of a transmitted PCS signal. Using this technique, we conducted a wavelength-division multiplexed transmission experiment with 32-Gbaud 16/64QAM-based PCS and a fixed FEC of a low-density parity-check code for DVBS-2, where the IR of PCS was optimized at each transmission distance. We confirmed that the data rate of PCS with a fixed FEC and DSP configuration could be improved up to 1.9 times compared with that of QAM-only rate adaptation and that 64QAM-based PCS could provide a wider range of transmission distance and IR while almost covering that of the 16QAM-based one.