The first ever attempt at fully autonomous dock-to-dock operation has been tested and demonstrated successfully at the end of 2018. The revolutionary shift is feared to have a negative impact on the safety of navigation and the getting of real-time situation awareness. Especially, the centralized context onboard could be changed to a distributed context. In navigation safety domain, monitoring, control, assessment of dangerous situations, support of operators of decision-making support system should be implemented in real time. In the context of autonomous ships, decision-making processes will play an important role under such ocean autonomy, therefore the same technologies should consist of adequate system intelligence. At the same time, situation awareness is the key element of the decision-making processes. Although there is substantial research on situation awareness measurement techniques, they are not suitable to directly execute quantitative processing for the situation awareness of autonomous ships navigation. Hence, a novel quantitative model of situation awareness is firstly proposed based on the system safety control structure of remotely controlled vessel. The data source is greatly limited, but the main result still indicates that the probability of operator lose adequate situation awareness of the autonomous ship is significantly higher than the conventional ship. Finally, the paper provides a probabilistic theory and model for high-level abstractions of situation awareness to guide future evaluation of the navigation safety of autonomous ships.