The law of three is that whenever something good or bad happens, three times in a
row, you really notice it. Especially if you are expecting something similar,
and if the things that happened have low probabilities.
Why is
it not law of four? Well, the probability is just that much less. All it takes
is three good or three bad or three whatever things in a row to grab your attention.

  1. Once is happenstance.
  2. Twice is coincidence.
  3. Thrice is conspiracy.
  4. (Four times is rare, I might add)

Why do we see this so often? Although the individual events are rare, the
probability is high that any one of the range of things we expect (bad things, good things, etc.)
will happen. And, when you are already expecting one of these
three-fold occurences, you will be looking out extra hard for connections.
Some would say that we actually play a role in helping these events happen,
consciously or not.