Measurement of subjective probability may theoretically be achieved based on the decision making tasks which require participants to choose between two gambles with known and unknown outcome probabilities. However, this approach is known to suffer from the effect of a human cognitive factor known as the ambiguity aversion. Moreover, because this approach is not based on statistical model, the estimation precision of the subjective probability cannot be evaluated. In the current study, we introduce the cumulative prospect theory model to this problem, and derive its Fisher information matrix. Using this information, we propose an adaptive presentation of the decision making tasks. Simulation studies and an empirical application confirmed that the derived Fisher information corresponds well with the empirical posterior standard deviation, and that the proposed adaptive task selection method performs much better than selecting the tasks at random. Furthermore, adaptive task selection which fixes the rewards of the two gambles was found to perform worse than the unconstrained ones. We conclude that unconstrained adaptive task selection is desirable for measurement of subjective probability under ambiguity.