"The probability . . . is currently zero." There are two problems with that sentence. The first is the word the. When you speak of Bayesian probabilities, you need to speak for yourself. Bayesian probabilities are subjective; they quantify beliefs. And since your beliefs may be different from mine, there is no "the probability" to talk about; only "my probability."
The second problem with your sentence concerns the words "currently zero." If your probability is currently zero, then it will always be zero, no matter what evidence may eventually be found. In other words, if your probability for something is 0, no amount of evidence that might come to light can ever influence your belief.
Not exactly correct. The whole point of Bayesian probabilities is that they are calculated as information and knowledge become available and they change as the same information and knowledge become available.
Yes, but in Bayesian inference, data update the prior multiplicatively (through the likelihood function). So, if
L(x) is the value of the likelihood function, given some new data
x, and your prior probability is 0, that data cannot change your probability, since 0 ×
L(x) = 0. In other words, if your prior probability is 0, no amount of evidence can ever change your mind; your opinion is immune to evidence.
Currently zero means at current knowledge and information levels of humanity, there is no ESP, nor any way to calculate its probability.
No. First of all your statement is self-contradictory: if there is no way to calculate a probability, then how can you say that the probability is 0? You can't, if you can't calculate it; and if you claim that it is 0, then you've just calculated it. Make up your mind!
Furthermore, a Bayesian probability of 0 for a hypothesis
H means that you think
H is absolutely impossible; not just impossible given current knowledge. If you hold a probability of 0 for
H you are essentially saying that not only does current knowledge exclude
H, but that there can never be any knowledge that permits
H. And again, it's just your probability, your belief. There is no one Bayesian probability of any hypothesis. Bayesian probabilities are people's subjective judgments about plausibilities, conveniently stated on a continuous scale from 0 to 1.
There is no set, and there is no hypothesis where ESP can exist based on our knowledge currently. Some day in the future that possibly may change.
If you believe that some day there could possibly be evidence supporting ESP, then your probability of ESP is not 0, whether you think it is or not.
But possibly isn't the same as a probability. There is no probability for ESP, although there is a remote possibility.
Look, if there is a possibility that something may be true, then there is a Bayesian probability that it is true, since all a Bayesian probability is is a quantitative statement about one's certainty that the thing is true. For ESP, my Bayesian probability is about 10^-7. YMMV.
Although it has been many years since I studied probabilities, I am pretty sure I am correct here. I thought about it for a while, and I suppose instead of zero it may be better to say undefined

, either way there is no calculated probability for ESP. Alien life though has a set and many good hypotheses that can work within the known laws of physics. This allows us to easily calculate a Bayesian probability but the accuracy of the calculation is still pretty poor without more precise information. Give us time.
You misunderstand the nature of Bayesian probability. I've tried to correct that a couple times now. The first time, you completely missed the point. Perhaps that was partly my fault for not explaining it better. Hopefully, I have done a better job this time.