On planet Brilliantia, there are two types of creatures: mathematicians and non-mathematicians.
Mathematicians tell the truth of the time and lie only of the time, while non-mathematicians tell the truth of the time and lie of the time.
It is also known that there is a chance a creature from Brilliantia is a mathematician and a chance that it is a non-mathematician, but there is no way of differentiating from these two types.
You are visiting Brilliantia on a research trip. During your stay, you come across a creature who states that it has found a one line proof for Fermat's Last Theorem. Immediately after that, a second creature shows up and states that the first creature's statement was a true one.
If the probability that the first creature's statement was actually true is , for some coprime positive integers , find the value of .