Are the molar extinction coefficient and cross-section of an absorption related to the probability of absorption?

I have struggled to find a formal definition of cross-section of absorption; from what I've gathered, its best defined as 'the intensity of absorption'.


Wikipedia's formal definition of the molar extinction coefficient is 'how strongly a species absorbs EMR at a given wavelength, per molar concentration'.


So how are the molar extinction coefficient and cross-section different? I presume that whilst the molar extinction coefficient remains constant for a given wavelength across all concentrations, the cross-section differs for a given wavelength with changing concentration. 


Is either the molar extinction coefficient or cross-section of an absorption equal to the probability that a single species absorbs a photon at any one point in time?


