Automated driving (AD) is likely to encounter situations, when vehicle control is handed from the system to the human driver. Such situation may occur, e.g., when a steadfast obstacle is suddenly detected in front of the moving vehicle, and emergency breaking is the only way to avoid collision. Probabilistic analytical modeling (PAM) is applied in this analysis to model the vehicle’s and the system’s performance for the given available sight distance (ASD) viewed as a non-random variable and with consideration of the driver’s human capacity factor (HCF). The general concepts are illustrated by numerical examples.