In the context of the recently derived probabilistic picture of in-medium jet evolution, we study radiative corrections which yield potentially large double logarithms, αsln2L, for large enough medium length L. We show that these large corrections are universal and can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. We argue that the probabilistic description of these phenomena remains valid, in spite of the large non-locality in time of the radiative corrections. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size L as L2+γ, with γ=2αsNc/π, as compared to the standard scaling in L2.