Now calculate the probability of the current Universe arising spontaneously from vacuum.
"Around this vast timeframe, quantum tunnelling in any isolated patch of the vacuum could generate, via inflation, new Big Bangs giving birth to new universes [...] this is also the time required for a quantum-tunnelled and quantum fluctuation-generated Big Bang to produce a new universe identical to our own, assuming that every new universe contained at least the same number of subatomic particles and obeyed laws of physics within the range predicted by string theory."
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Given that the question asks about 'current' universe arising spontaneously from vacuum the probability is 1 because that has already happened.
The more interesting question, what is the probability of a new universe similar to our own arising. To the best of our knowledge (which for this type of extrapolation is admittedly flimsy) this is also 1, this just takes a very long time. The expected time it would take (10^10^10^56) is specified on the last row on the "Future of the Earth, the Solar System and the Universe" table.
Well, we don't know that. Whatever 'came before' (if that even makes sense) probably wasn't a vacuum with the same rules as we see now.
Only if you meant "could have happened, but did not, and now for some reason can no longer happen."
"All events that could have happened, but did not" would reasonably encompass every event with 1 > P > 0, wouldn't it?
Actually, no. That would be the existence of my own consciousness. Just mine. Not yours. That's it.
I believe it's well-established that elementary particles can spontaneously generate through quantum fluctuation. Assuming that this process is uniformly distributed, the probability per unit time of any given structure self-generating is nonzero (if fantastically small). Over a long enough timescale, the probability of any possible event occurring approaches one. If time is infinite, the probability is one.
What am I missing?