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The probability in question is applied to the second choice, not the initial choice. You're maintaining the initial probability throughout, but it's changed by Monty giving you a second choice after the initial condition has changed.
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Knowing that death is certain and that the time of death is uncertain, what's the most important thing?
—Bhikkhuni Pema Chödrön
Humankind cannot bear very much reality.
—From "Burnt Norton," Four Quartets (1936), T. S. Eliot
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