Trust plays a decisive role in the public's acceptance of the new self-driving car technology. In order to better understand how to promote confidence in vehicle automation safety among the public, we studied pedestrian behavior shortly before and while crossing a marked crosswalk. Such information is also essential for setting parameters for automated vehicles to act accordingly during interactions with pedestrians. Through the analysis of the recorded videos and subjective qualitative data, we identified factors that potentially influence the perception of a road situation as safe in an environment in which vehicles operate with full driving automation (level 5) in a public space. A variety of responses were observed that exhibit several levels of trust, uncertainty and a certain degree of fear. It became clear, however, that the longer the people interacted with the vehicles, the more confident and trusting they became in automation capabilities. The existence of a communication system to interact with driverless vehicles was also evaluated as positive.