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A consistent description of transitions to improved confinement regimes in terms of a probabilistic transport model is presented. The model has two thresholdlike mechanisms, acting, respectively, on the first and second spatial derivatives of the density. These mechanisms allow switching between three different transport channels: one corresponding to classical diffusion and the other two to different scale-free transport mechanisms. The dependence of the transport properties on the second derivative models the appearance of a sheared radial electric field that causes a reduction of transport. The results of the model reproduce the enhancements of confinement time and fluctuations (associated to edge localized modes) that take place during transitions, when the fueling rate is increased. The model could be of relevance beyond the field of plasma physics as a general transport model with critical parameters.