in other words, what is the probability of passing this test by random guessing? Is it like one out of eight or more like one out of 1024?
Or do the people involved keep this issue secret?
Well, people pass it. Presumably, for those who do not believe people are able to perform miracles, that would be some strong evidence that, in fact, it is not so probabilistically difficult for the test to be passed, either because the test in itself is not so difficult, or because the test is administered to enough people that it becomes likely one will pass.
(Disclaimer: I do not know anything about the specifics of this test. I am only commenting on the basic presumptions of the OP.)
Success by random guessing in a test in which the chances of success by random guessing is 1 in 1,024 is not, by any definition, “miraculous”. Coincidence =/= miracle.
Why ask the question? Does it matter to those who administer the test whether success is acheived “miraculously” or otherwise? Does anybody claim that there is a miracle involved?