I think there is no such thing as a conditional random variable. There are conditional probability distributions, but I've never heard of A|B itself being a random variable and I think it doesn't fit the definition. A random variable (I'm not a mathematician) is a function that takes an elementary event and returns the value of the variable.
You may say this is pedantry, but I think it's important to keep track of what is what, especially when being a beginner. You can afford to be sloppy once you're more advanced.
You may say this is pedantry, but I think it's important to keep track of what is what, especially when being a beginner. You can afford to be sloppy once you're more advanced.