I think I have seen in some mining models there is an option for individual confidence value for each predicted class attribute. However, is there a general way, let's say a node, to see these individual confidece values for predictions independent of the model options.
What I meant was the option might not have added to the each individual models (which seems the case) but like the Statistics node we may be able to get the p values for each individual prediction, probably with a complimentary node.
I remember confidence values for predictions to be provided in SPSS Modeler (automatically, if the option selected), almost for all classification models. Actually, I had that in mind when I raised whether a similar approach is possible in Knime or not.
Typically, p-values hinge on assumptions about underlying probability distributions related to hypotheses, neither of which mining algorithms typically make - so there's no meaningful definition to begin with.
Your best bet would be bootstrapped confidence intervals for regression predictors (based on which you can derive p-values), or using the "Crosstab" node for scoring classification. Unlike the traditional scoring nodes, it gives you a a p-value for the "no association" null hypothesis based on the Chi-square statistic.