Monkeys & typewriters - original point?

When I looked at the Monkey Shakespeare Simulator the other day, I remembered how we traced the story/image back to mathematician Emile Borel of 1913 (1), and it occurred to me to wonder what point Borel was trying to make when he invented it as an analogy or illustration.

The only other thing I remembered about Borel was that he was the one who said that events of extremely low probability are the things that don't happen by chance. That doesn't seem to match any blithe prediction of monkeys producing Hamlet.
Borel's paragraph, in French, is found here:
http://www.angelfire.com/in/hypnosonic/Parable of the Monkeys.html

After describing the imaginary set-up of a million monkeys turning out results and these pages being bound (by unreading humans) into books, which turn out to replicate the world's libraries, he says

Telle est la probabilité pour qu'il se produise
pendant un instant très court, dans un espace de
quelque étendue, un écart notable de ce que la
mécanique statistique considère comme la phénomène le plus probable...
The meaning of which is difficult for me to puzzle out, and the English translations are also hard:
Saved from Message-ID Such is the likelihood that there should occur,
even for a moment, a notable deviation in any extended region from what statistical mechanics considers the most likely phenonenon ...
This one I saved from an old Web page, not found now, looks like Babelfish nonsense:
Such is the probability so that it occurs during one very short moment, in a space of some extent, a
notable variation of what statistical mechanics
regards as the phenomenon most probable."
I hope that Isabelle or other fluent French speakers can help here.

However, as best as I can figure, Borel is talking about how unlikely this all is. Isn't he saying, "It's about as unlikely that these randomly-produced pages will turn out to reproduce all the world's literature, as it is for the laws of science to be suspended, even for an instant"?
The chances of the monkeys' work reproducing the world's literature is incredibly tiny. The chances of events deviating from the laws of statistical mechanics is similarly tiny.
I can't find the larger piece of writing this is from, so I don't know what sort of event of "statistical mechanics" he was considering. I wonder if it was the sort of question like, "Since atoms move, could all the atomic particles in my finger and this door happen to move aside at the same instant, so my finger goes into the door?"

So although Borel (apparently) invented this image of the typing monkeys, it would have been some later variant that gave us what we know today, the claim that if this could be set up, the works of Shakespeare would eventually be produced.
The next known use was Eddington (1929) (2), and he too was cautious, using it as an illustration that this unlikely event was more likely than molecules lining themselves up:
... If I let my fingers wander idly over the keys of a typewriter it /might/ happen that my screed made an intelligible sentence. If an army of monkeys were
strumming on typewriters they /might/ write all the books in the British Museum. The chance of their
doing so is decidedly more favourable than the
chance of the molecules returning to one half of the vessel.
So, my point is, it began as a measure of *unlikeliness.* Not as a way to illustrate infinity or anything else.
I see that the third example on the Parable page, Jeans (1930), attributes it to Huxley and uses the words "bound to produce"... And so the image, once launched, gathered steam and changed.

I am reminded that "In 1911 Boas casually mentioned that Eskimos used four unrelated words for snow..." (Pinker 1994)
(1) Émile Borel, "Mécanique Statistique et Irréversibilité," J. Phys. 5e série, vol. 3, 1913, pp.189-196.
(2) A. S. Eddington. The Nature of the Physical World: The Gifford Lectures, 1927. New York: Macmillan, 1929, page 72.

Best Donna Richoux