Coincidental phone call and odds

We used to phone some friends about once every 1 to 3 years. We sat down one evening and decided it was time to ring them. We did so and they were engaged. Sure enough, when we rang a second time and chatted we discovered they had tried to ring us and we were engaged! This was in the time preceding digital exchanges. We have no idea how long (in seconds) that this sort of simultaneous dialling would cause an engaged tone, but let's assume 1 second. We usually rang them after a year, but before, say, three years. So that was about a one second chance in two years. Assuming we would ring some time during the evening, then that is one second in 2 years x 365 days x 3 hours x 60 minutes x 60 seconds which is a chance of 1 in 7884000 !! Much better than winning the lottery :-) Spookily, I turned the TV on one Sunday evening (several years after the above) and channel hopped. As I switched to the BBC I heard the name of the same person with whom we had the coincidence above. It turned out he was representing the Navy at the annual Festival of Remembrance Service at the Royal Albert Hall. I cannot calculate the odds of that - there are quite a few factors to consider. But I know it was high!