Well, if p(x next month) = .995 then p(x next week) < .005, so your odds possibly went down.
If, on the other hand, p(x before the end of next month) = .995, then p(x next week) may be > .005
The short answer is that there isn’t enough information in the problem description. Your priors are incorrect, incidentally; they should match historic data. If p(x) is always 50%, this implies that p(x next week) and p(x within the next year) are identical, which cannot be the case, because the latter probability includes the former. p(x within the next year) > p(x next week).
Your best strategy is to examine historical data, and see what the odds of a prime minister, once specifying a time frame for retirement, actually meeting that time frame are.
Well, if p(x next month) = .995 then p(x next week) < .005, so your odds possibly went down.
If, on the other hand, p(x before the end of next month) = .995, then p(x next week) may be > .005
The short answer is that there isn’t enough information in the problem description. Your priors are incorrect, incidentally; they should match historic data. If p(x) is always 50%, this implies that p(x next week) and p(x within the next year) are identical, which cannot be the case, because the latter probability includes the former. p(x within the next year) > p(x next week).
Your best strategy is to examine historical data, and see what the odds of a prime minister, once specifying a time frame for retirement, actually meeting that time frame are.