Assuming your math is correct (I didn't bother to check it), that would be the odds of a random server failing in a random 20 second interval.
You didn't pick a random server, you picked one already known to have crashed. And you didn't pick a random 20 second interval either. The odds of that server crashing in that 20 second interval was 100%, because it was already known to have happened.
This is a classic mis-application of statistics.
Admittedly, the interval right at New Year's is a bit suspicious, since there is some specific code to handle leap years, etc. But given that there wasn't a rash of outages reported, I am going along with the coincidence theory.