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A methodology is presented to investigate the recurrence of extraordinary events. The approach is fully general and complies with a canon of inference establishing a set of basic rationality requirements scientific reasoning should satisfy. In particular, we apply it to model the interarrival time between disastrous oil spills in the Galician coast in the northwest of Spain, one of the greatest risk areas in the world, as confirmed by the Prestige accident of November 2002. We formulate the problem within the logical probability framework, using plausible logic languages with observations to allow the appropriate expression of evidences. Therein, inference is regarded as the joint selection of a pair of reference and inferred probability distributions, which better encode the knowledge about potential times between incidents provided by the available evidences and other higher-order information at hand. To solve it, we employ the REF relative entropy method with fractile constraints. Next, we analyze the variability of the joint entropic solution, as knowledge that a time has elapsed since the last recorded spill is added, by conditioning the evidences. Attention is paid to the variability of two representative parameters: the average reference recurrence time and an inferred characteristic probability fractile for the time to an event. In contrast with classical results, the salient consequence is their nonconstancy with the elapsed time and the appearance of a variability pattern indicating an observational memory, even under the assumption of one-parameter exponential models, traditionally regarded as memoryless. Tanker accidentality is therefore dynamic, changing as time goes on with no further accidents. Generality of the methodology entails that identical conclusions would apply to hazard modeling of any other kind of extraordinary phenomena. This should be considered in risk assessment and management.