What does Luke 1:9 mean?

In one sense, the number of priests serving in the temple would have been limited. Only a single "division" of priests served at a time (Luke 1:8; 1 Chronicles 24:10). The 24 divisions all came from the lineage of Aaron, of the tribe of Levi. As compared to the full population of Israel, this would have left a relatively tiny portion directly serving in the temple at any given time.

And yet, there were not that many tasks to be performed on a regular basis. Some rites were done more often than others. All were considered an honor (Joshua 18:7), some more than others. The twice-daily offering of incense seems to have been one such honor (Exodus 30:1–8). For that reason, it seems random chance (Luke 1:8) was used to decide who would perform this task. Scholars indicate a given priest may have performed this sacrament once—if that—in their entire life. This may be the case for Zechariah. If so, the timing of God's vision and prediction are further proof of their miraculous nature (Luke 1:11).