Each shuffle of a deck of cards has an outcome which is one in 52! (That's 52 factorial, which is 8.06581752 × 1067.) It's a huge number. For comparison, the estimated number of stars in the universe is "only" 1021. Source: this NASA website.
So the odds against any particular card shuffle are truly beyond astronomical. Yet, if you go ahead and shuffle a deck ... ta-DA! There it is. You've obtained a virtually impossible outcome. Similarly, the odds against the history of England being what it has been are probably even greater (I wouldn't even guess at how to quantify that).
The point is that computing the odds against such things doesn't do much for you -- especially when you're dealing with events that have already happened, when the events have become a 100% certainty. I've labeled this kind of thinking the fallacy of retrospective astonishment. It applies to the existence of each of us, when you consider the odds against each specific conception for each of your ancestors. And it also applies to the development of the presently-existing biosphere on Earth.
One can, if so inclined, see the hand of Providence in each such outcome. Or not (as each step along the way is a natural event). There's no scientific answer to such speculations. But there's always Occam's Razor.
Yet here we are. Just like a shuffle of a deck of cards. We're highly improbable. If it were to start all over again, some other shuffle of the cards would take our place. We're unique. Never to be repeated. Irreplaceable. Priceless.
First, pull some numbers out of your arse ...
But the vast majority of those 52! hands are nothing special, and there are only a few "extraordinary" hands. For example getting all the cards in strict order of suit and number would be an extraordinary hand, and would be astonishing retrospectively without being a fallacy.
This is similar to life. The vast majority of nucleotide combinations are no-results. A very few lead to functional proteins. So we could say there is an extraordinary hand in life.
But astonishment at this is another thing. It would be astonishing to think chemistry could have dealt such an extraordinary hand if chemistry was random. But it isn't, so there is no necessary reason to be astonished by it.
So I think the fallacy being committed is more like "fallacy of astronishment where no astonishment is necessarily due".
Well, on another thread, someone claimed that numbers bigger than 1050 were impossible; that would affect the history of England a bit. Of course, if the French hadn't won at Hastings, we'd all be speaking English now.