I'm walking down a street in Bangkok and I bump into a colleague from my place of work in the UK. I'm hiking in the hills near Kathmandu and meet someone from my birth town. A friend take a flight and ends up sitting next to the mother of someone in his daughter's class at school. What are the odds?
When we think about calculating the probability of this happening, by factoring in things like 'what is the probability that the mother was taking this flight', 'what is the probability that she would have the seat next to me', etc., we often think that we are dealing with extremely small probabilities. But like the famous birthday pairs question, this overlooks an important part of the coincidence.
The odds to be calculated are not the odds of the specific incident, but the odds of something remarkable happening. In other words, I would be equally likely to report as 'amazing' sitting next to the mother of my child's classmate, sitting next to someone from my home town, sitting next to someone who bought a lamp at my garage sale, etc. The space of things that we would consider remarkable is actually far larger than we think, especially when we are confronted with a specific case.