Interesting post. I take the point that synchronous and coincidental are not exact synonyms. Synchronicity implies a deliberate and pre-planned connection between events, designed to make people think there is some hidden meaning. If there is such a direct connection between events, then that is organised, or intended, by a human agency. If they just happen to look as if there is meaning there, then the explanation is that, well, it just happened to appear as if it was planned ... ... always after the event f course ...
Such things appeal to our sense of patterns, symmetry, balance etc, but there are no hidden meanings there. Any meanings are imagined.
If something supremely improbable happens, then it still has a probablity of 1, because it has happened. Whatever the odds are, if it happens, it immediately changes the odds from XXX-0 to XXXX-1 - or something like that!