Can someone please explain how to find the 0.998 at the end using the numbers given?

I need to this same problem assuming an equal-probability prior. In other word p=0.5, not p=51/(51+14) which means p=0.78.

I think my formula will be the same as the one at the end, but when I use p=0.5 or p=0.78 I am getting crazy numbers (I should be getting 0.998 when I am using p=0.78 as that is the solution given here).