TSR's Marvel Superheroes game uses a universal table that makes fairly clear what the probabilities are. What is important for some people is that the table uses percentile dice and a lookup that slows the game down. Alternate dice approaches are therefore considered. The basic result table is given below, along with a text table that shows the chances of each color result.

Notes that the probability of a Green result is always 30%. Thus, a Yellow or Red result always happens when the minimum success chance is exceeded by 30. The Red success chance is more complex, but is roughly onefifth of the total chance of (Yellow + Red). Below is a graph of the probability of a Red result as a fraction of all Yellow or Red results. That is, what fraction of (Yellow or Red) successes are Red. The fraction increases from roughly 10% to 38% as the rank increases.
Som people have had some issues with this roll procedure, because it requires both a double die roll as percentile and a table lookup. One suggested approach for this is to write in the break points for the die roll with each ability. So if you have an ability at Remarkable, then you would write beside it on the character sheet 36, 66, and 95.
Another option is to simplify the table into a simpler die roll. You could instead roll both 1d20 and a 1d6 at the same time. The d20 is checked against a target number, and if it beats the target number by 6 or more, then it is at least a Yellow Result. If in addition there is a "6" on the 1d6 (or 56 for Rank Monstrous and up), then the result is Red. The resulting chances are quite close to the official table, while most likely simpler to implement at the table.
Rank  Value  d20 Target  Official Cum. Chance  Simple d6 Chance  

Green  Yellow  Red  Green  Yellow  Red  
Shift 0  0  14  35%  5%  1%  35%  5%  1% 
Feeble  2  13  40%  10%  1%  40%  10%  2% 
Poor  4  12  45%  15%  1%  45%  15%  3% 
Typical  6  11  50%  20%  3%  50%  20%  3% 
Good  10  10  55%  25%  3%  55%  25%  4% 
Excellent  20  9  60%  30%  6%  60%  30%  5% 
Remarkable  30  8  65%  35%  6%  65%  35%  6% 
Incredible  40  7  70%  40%  10%  70%  40%  7% 
Amazing  50  6  75%  45%  10%  75%  45%  7% 
Monstrous  75  5  80%  50%  15%  80%  50%  17% 
Unearthly  100  4  85%  55%  15%  85%  55%  18% 
Shift X  150  3  90%  60%  20%  90%  60%  20% 
Class 1000  1000  2  95%  65%  25%  95%  65%  22% 