Probability Question I'm sorry but I don't see any absurdity.
Each one of these probabilities (use the variable p) can be such that
1. p = 50% (agnostic)
2. p < 50% (unlikely)
3. p > 50% (likely)
Note that
There are 3 values to consider [p is P(E) or P(H/E) or P(H)] to calculate P(E/H) and so there should be
possibilities to calculate. Lemme calculate two of these possibilities (
vide infra)
1. P(E) = 50%; P(H/E) = 50%; P(H) = 50%
i.e. we have to be agnostic about it.
2. P(E) = 50%; P(H/E) < 50% (let's say it's 40%); P(H) = 50%
i.e. its unlikely.
So on and so forth ...
For different time frames e.g. in the next 10,000 years, in the next microsecond, etc. we can scale up/down the probability we assign to P(H) = aliens will contact us in the next 10 years. For example the suppose P(H) = 20%. Then the probability that aliens will contact us in the next 5 years will be 10% [5 years is half of 10 years; I'm assuming that the probability of contact increases with time].
N. B. Scaling up can sometimes lead to percentage probabilities > 100%. These should all be made = 100%.
For example, given that the probability of contact within the next 10 years is 70%, what is the probability of contact in the next 100 years? 70% × 10 = 700%. Probabilities can't be > 100%. You'll have to go with 100%.