(1) You have numerical values, then pick a classifier and let it do the job and learn how v21 affects the system. I think decision tree is the logic choice here. Next logic choice is neurofuzzy.

(2) For calculating the probabilities, just do the Bayes rule math: P(Y=poor|v21=high, v1=high, v2=high, v3=high, v4=high). 

You have two options:

1.  Adding the new variable v21 to training data and then re-running Random Forest algorithm.

2. Using decision tree first on new variable v21 and second running Random Forest algorithm.

Cheers

If you do not want to change your current classifier for V1 to V20, then you might leave it as it is and design a new classifier whose input is V21 and the output (call it O20) of the original classifier operating on V1 to v20. That should be easy to do because you have just two inputs, O20 and V21, and just two classes, good and bad.

You can think of it as information fusion. You are then fusing the "expert" opinion based on V1 to V20 with the additional information provided by V21.

Ron