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According to the Novikov's self consistency principle (also proposed by other authors such as Kip S Thorne) 1 2, if an event exists that would cause a paradox or any "change" to the past, then the probability of that event is zero.

But is the probability of that history exactly zero, or very close to zero? (i.e extremely unlikely to happen but not strictly impossible)

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I think that the notion of an "inconsistent history" isn't even well defined in this picture, so it's vacuous to say that they have probability zero. In any case, inconsistent histories don't happen.

The paper coauthored by Novikov says in its abstract:

[The] principle of self-consistency [...] states that a local solution to the equations of physics can occur in the real Universe only if it can be extended to be part of a global solution, one which is well defined throughout the (nonsingular regions of) classical spacetime.

This makes no mention of probability.

The probabilistic version of the principle in the Wikipedia article goes all the way back to the very first revision from 2002. The only reference in that version was to a short speech by Novikov that also says nothing about probability. I think the probabilistic version was probably invented by the Wikipedia editor, and you can safely ignore it.

Novikov's speech seems like a good introduction to the principle as he envisioned it.

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