Sforno on Deuteronomy 21:5/ספורנו על דברים כ״א:ה׳

1לשרתו ולברך, the (Temple) service of the priests is instrumental in attaining expiation for the innocent blood spilled, and in securing blessing for the land.

2ועל פיהם יהיה כל ריב וכל נגע, so that they are familiar with the psyches of the people and their norms, as they observed already by watching their fathers deal with such matters. Perhaps, due to such cumulative empirical knowledge they have some knowledge of whose character has been tainted by sin so that such intuitive knowledge will help them bring the truth to light. (in the investigation of the murder)