Debra and I went to Phoenix last week to attend a court hearing (a family matter), and to get some things she had in storage. The trip itself was not exceptional except for one thing.

When we arrived at the court house on Tuesday, Debra went to the information desk to find out which room the hearing would be held in. I was seated not far away answering a work-related mail message on my phone, but within earshot. I could hear that people were talking and even pick out Debra’s voice, but I wasn’t paying attention to what was being said. But then I heard another voice that I sounded very familiar.

When I looked up Debra was walking away from the information desk, and the familiar voice was coming from a Sheriff’s deputy at the desk who was looking in her direction: from my perspective facing more away than in exact profile. I suppose you could say that I was seeing his right rear quarter.

The voice, combined with the profile and the uniform, prompted me to walk toward him and say, “Bob?” He turned around and, sure enough, the deputy was indeed Bob: a guy I knew in military school. We’d met at a few reunions since then, and when I saw him eight or ten years ago he was a deputy with the Maricopa County Sheriff.

We chatted for a while and marveled at the unlikely meeting. Bob’s take on things was “It’s a small world,” and I couldn’t disagree.

But on the way back from the hearing I got to wondering, “what are the odds?” More precisely, what was the probability that I would run into that person at that time. At first it seemed highly unlikely, but then I did a little calculation.

The number of Sheriff’s deputies in Maricopa County is something less than 1,000. If you assume that we had to encounter a deputy, then the odds of it being Bob were, at worst, one in 1,000. That’s not so very unlikely. If you narrow it down to deputies who have that court duty (probably fewer than 100), then it’s only one in 100. And if you restrict it to deputies who have duty in that particular court building, then it’s probably better than one in ten.

Given the conditions, that I ran into Bob is not terribly surprising. It wouldn’t seem surprising at all if I lived in Phoenix and knew that his current assignment was at that building. In fact, I probably would have been looking for him when I entered the building and might even have been surprised if I didn’t see him.

Mathematics aside, a seemingly random encounter with an old friend was a pleasant surprise.