First, write out what you know.
Total: 12
Green: 3
Red: 4
Blue: 5
Cool. Probability is "how likely", so how likely is it for you to pick a green cup? Well, if you pick any other cup, then it's not green, so you know they can't be the case. How many green cups are there? 3. 3 is the denominator of your probability.
If you're picking the cups out of the total, which is 12, then your answer should be 3/12, which can be reduced to 1/4 :)