There has been some time that Light detection and ranging (LIDAR) technologies receive much attention due to its capability of enabling applications such as Advanced Driver Assistance Systems (ADAS) and Simultaneous Localization and Mapping (SLAM) etc. Meanwhile, Single-Photon Avalanche Diode (SPAD) is a very attractive choice as light detectors in LIDARs because of its high sensitivity. However, LiDARs in ADAS need to work in adversary environments such as fog, rain, snow or haze, and successful signal detection requires solving issues such as extremely low signal levels and noise due to background illuminance. In this paper, a SPAD-based LIDAR system is described and a probabilistic model of received photons is introduced. Furthermore, the model is generalized for SPAD detectors operating in fog conditions. As for signal detection, a basic signal detection algorithm using Likelihood Ratio Test (LRT) is developed. Two more approaches of signal detection are introduced to cope with fog conditions. Simulations and experiments are provided to illustrate our points.