I had been solving Bad Luck Island and I wrote this formula for calculating the probability of meeting for example Rock and Paper :

rsp = r + s + p;
rs = r + s;
rp = r + p;
sp = s + p;

P_rp = (r/rsp) * (p/sp) + (p/rsp) * (r/rs);

I figured out that it is wrong, but I want to know why and What am i calculating here ?!

because when i use this formula for all 3 possible meetings , and sum up them , it equals to 1! and I don't know what is the meaning of this formula !!!

( sorry if it is a stupid question! )