Technologies and techniques for detecting a parking space becoming available via an assistance system of a vehicle searching for a parking space. Radar signals are emitted by at least one radar sensor searching for the parking space and whether a parking space becoming available is recognized on the basis of received radar signals, which are evaluated by an evaluation unit of the vehicle. Micro-movements of a vehicle parked in a parking space, may characterize the vacating of the parking space, and may be detected by evaluating the radar signals reflected by this parked vehicle. A presumptive parking space becoming available may be identified by the assistance systems on the basis of such a detection of a micro-movement. An assistance system and a motor vehicle using the assistance system are also disclosed.