Adam Clarke on Luke 10:31

And by chance - Κατα συγκυριαν properly means the coincidence of time and circumstance. At the time in which the poor Jew was half dead, through the wounds which he had received, a priest came where he was. So the priest's coming while the man was in that state is the coincidence marked out by the original words.

Priest and Levite are mentioned here, partly because they were the most frequent travelers on this road, and partly to show that these were the persons who, from the nature of their office, were most obliged to perform works of mercy; and from whom a person in distress had a right to expect immediate succor and comfort; and their inhuman conduct here was a flat breach of the law, Deu 22:1-4.