The random utility model (RUM) is a fundamental notion in studies of human decision-making. However, RUM relies on the calibration of its choice function's weight parameter, usually interpreted as a rationality parameter, resulting in a case-dependence that undermines both interpretability and predictability of choices across experimental settings. We addressed this limitation by normalizing utilities in RUM and deriving a new choice parameter β, independent of case-specific prospects. Drawing from a novel interpretation of β in terms of the lowest perceived probability of unlikely events, we conducted an experimental survey in Swedish universities to infer β distributions, capturing the variability of probability perception among decision-makers. We tested these statistical models for β on two independent datasets exploring the framing effect. The results showed that the predictions align with the observed experimental data (Pearson's correlation greater than 94%), thereby indicating that the novel characterization of the choice parameter strengthens the predictive capabilities of RUM.