During the last debate, Gandalf says:
"Concerning this thing, my lords, you now all know enough for the understanding of our plight, and of Sauron's. If he regains it, your valour is vain, and his victory will be swift and complete: so complete that none can foresee the end of it while this world lasts. If it is destroyed, then he will fall; and his fall will be so low that none can foresee his arising ever again. For he will lose the best part of the strength that was native to him in his beginning, and all that was made or begun with that power will crumble, and he will be maimed for ever, becoming a mere spirit of malice that gnaws itself in the shadows, but cannot again grow or take shape. And so a great evil of this world will be removed."
How does Gandalf -or any other of the wise- know that Sauron will indeed be crippled to such an extent if the ring is destroyed (and why is this not already mentioned during the council of Elrond)?
To understand where this question comes from, it may be useful to know that Peter Jackson's depiction of Sauron's incapacitation at the end of the Second Age is controversial. It is not said in the books that a fit Sauron has his ring-finger cut of and then suddenly disintegrates. The text rather suggests that Gil-Galad and Elendil maim Sauron, whereafter Isildur cuts the ring off a near-incapacitated Sauron.
It was brought to my attention that this question may superficially be viewed as a duplicate of this one. However, that question does not ask after the method by which the wise determine that Sauron will be crippled by the ring's destruction. That is, it asks whether, not how. I find this important because during the last debate Gandalf urges the leadership of Gondor and Rohan basically to bet everything on this single assumption. So one would think/expect that Gandalf has solid proof for his assertion.