This paper develops a binary choice model in light of the notion of probabilistic preference and/or indifference in the preference structure within an information processing framework. Two thresholds based on the difference in utility from two alternatives are theorized to help articulate ordinary, day- to-day choice situations more realistically. The three states including “indifference” replace “preferences” between the stages of simple perceptions and choice. Further, five postulates are formulated based upon the two thresholds, hence the corresponding conditional probabilities derived. These two thresholds with the five postulates are incorporated into the conventional probabilistic choice model. Accordingly, the marginal distribution for the three states are derived. This theoretical model of two thresholds contributes to theorize probabilistic choice as the outcome of probabilistic preference and indifference. The model is applied to a simple capital investment problem based on Net Present Value for the estimation of two parameters, i.e., the two thresholds