Context. Open clusters that emerged from the star-forming regions as gravitationally bound structures are subjected to star evaporation, ejection, and tidal forces throughout the rest of their lives. Consequently, they form tidal tails that can stretch kiloparsecs along the cluster’s orbit. Aims. Cluster members are typically found by searching for overdensities in some parameter space (positions and velocities or sometimes actions and orbital parameters of stars). However, this method is not effective at identifying stars located in the tidal tails far from the open cluster cores. We present a probabilistic method for finding distant cluster members without relying on a search for overdensities and apply it to 476 open clusters. Methods. First, we simulated the dissolution of a cluster and obtained a probability distribution (likelihood) describing where cluster members are to be found. The distribution of stars from the Gaia DR3 catalogue in high likelihood regions was then compared to the simulated stellar population of the Galaxy to define the membership probability of each star. Results. The survey of cluster members included all stars with a magnitude of G < 17.5 and larger clusters with an age of > 100 Myr within 3 kpc from the Sun. We successfully found stars with high membership probabilities in the tidal tails of most clusters. The recovered tidal tails stretch more than a kiloparsec from the cluster cores in some cases. We analysed the morphological properties of the tidal tails and demonstrated how properly normalised membership probabilities aid systematic studies of open clusters. Finally, we have published a catalogue of stars found in the tidal tails.