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

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).