Detectors based on single-photon avalanche diodes (SPADs) operating in free-running mode surfer from distorted detection signals due to the impact of afterpulse, dead time, and the non-linear detection efficiency response. This study presents a correction method based on conditional probability. In the experiments with high temporal resolution and huge dynamic range conditions, this method's residual sum of squares is near 68 times smaller than the uncorrected received data of SPAD and near 50 times smaller than deconvolution method. This method is applied to polarization lidar and CO2 lidar, and the performance shows significant improvement. This method effectively mitigates the impact of SPAD afterpulse, dead time, and detection efficiency non-linear response, making it suitable for all SPADs. Especially, our method is primarily employed for atmospheric detection.