-0.000081
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Putin has ruled for 25 years (ignoring Medvedev's "presidency"). Considering Russian rulers back to 1276, there are 14 who have served longer than 25 years. Their mean reign has been 33 years. If we assume the mean outcome for Putin is to serve for 33 years, with equal probability to fall at any time until that time, then the time from now to May 1st 2024 is 1.6% of the remaining 8 years.
Putin is 71 years old, and has access to unlimited healthcare resources. We can assume his healthcare will be at least as good as that of an average American. Social Security Administration actuarial data gives a 71 year old 2.8% chance of mortality in the following year. The time until May 1st 2024 is 48 days. (48 days / 365) * 2.8% = 0.37% chance of dying.
Putin's 25 year reign is roughly 25*365=9125 days. By Laplace's rule, the probability he will fall tomorrow is 1/9127. Considering the equivalent probability for each day from now until May 1st 2024 gives 0.52%