Recent gravitational-wave transient catalogs have used pastro, the probability that a gravitational-wave candidate is astrophysical, to select interesting candidates for further analysis. Unlike false alarm rates, which exclusively capture the statistics of the instrumental noise triggers, pastro incorporates the rate at which triggers are generated by both astrophysical signals and instrumental noise in estimating the probability that a candidate is astrophysical. Multiple search pipelines can independently calculate pastro, each employing a specific data reduction. While the range of pastro results can help indicate the range of uncertainties in its calculation, it complicates interpretation and subsequent analyses. We develop a statistical formalism to calculate a unified pastro for gravitational-wave candidates, consistently accounting for triggers from all pipelines, thereby incorporating extra information about a signal that is not available with any one single pipeline. We demonstrate the properties of this method using a toy model and by application to the publicly available list of gravitational-wave candidates from the first half of the third LIGO-Virgo-KAGRA observing run. Adopting a unified pastro for future catalogs would provide a simple and easy-to-interpret selection criterion that incorporates a more complete understanding of the strengths of the different search pipelines.