We apply previously developed Chu space and Channel Theory methods, focusing on the construction of Cone-Cocone Diagrams (CCCDs), to study the role of epistemic feelings, particularly feelings of confidence, in dual process models of problem solving. We specifically consider "Bayesian brain" models of probabilistic inference within a global neuronal workspace architecture. We develop a formal representation of Process-1 problem solving in which a solution is reached if and only if a CCCD is completed. We show that in this representation, Process-2 problem solving can be represented as multiply iterated Process-1 problem solving and has the same formal solution conditions. We then model the generation of explicit, reportable subjective probabilities from implicit, experienced confidence as a simulation-based, reverse engineering process and show that this process can also be modeled as a CCCD construction.