In this paper, we consider two independent k-record sequences with the same distribution. We determine the closeness probability of k-record values to a specific progressive Type-II censored order statistic. With this in mind, we first derive the exact expression for the Pitman closeness of records in general, and some special properties of the closeness probability are presented. Then, we apply the obtained results for the standard uniform and exponential distributions and exact expressions for the Pitman closeness are obtained. Finally, numerical results are displayed in figures.