I understand the principles of conditioning and its rules, but when do I decide if a problem will be easier using conditioning versus determining through other methods? I'm teaching myself probability and the whole concept of conditioning is kind of foreign to me. If somebody told me to solve a problem using conditioning then I could do it, but if I'm given a problem then conditioning is usually the last thing I think of to try to solve it.
An example: The textbook I'm using gave a problem where you were trying to find $P(X>Y)$ for two independent distributions $X$ and $Y$. I tried to show this algebraically using the pmfs (which could be found based on the information about the distribution given in the problem), but the solution in the book shows that I was "supposed" to condition with $\displaystyle\sum_{n=0}^{\infty} P(X>Y|Y=y)P(Y=y)$. I guess I'm unclear on when to use conditioning and what kind of clues there are in problems to tell me when conditioning is necessary.