Brief encounter at a railway station

I was walking along a side street by Waterloo Station during one of my rare visits to London when I was waylaid by a burly young man in a tabard collecting for charity. Being charitable and in no hurry I stopped to talk to him. He told me about how the charity helped young people who had got into bad ways to find a better life. He said that he had been helped in this way after a somewhat shameful past life and was being trained in computer technology at a college in Canterbury. I mentioned that a man with whom I had worked closely in an office in Tunbridge Wells had later left that job to set up a training course in computer technology at that same college. It turned out that this young man's tutor at the college was my former work colleague. After this discovery we parted company like good friends and I never did give him any money for his charity, but it didn't seem to matter to him any more. So, two complete strangers meet outside a very busy railway station in London, talk for just a couple of minutes and establish that they both know the same person well from encountering him in different circumstances in different towns. What are the odds of firstly their both knowing that same person and secondly their discovering it during such a brief encounter?