In a series of recent experiments anomalously large probabilities of laser-induced double ionization of the He atom have been observed. In this letter we analyse the clearest observation of this phenomenon, over a signal range of many orders of magnitude, by Walker et al. The analysis is carried out using a newly developed intense-field many-body S-matrix theory. For the first time good agreement between the experimental data and a theory is found. It is shown that the dominant mechanism behind the observed large probability of laser-induced double escape is a quantum mechanical process of absorption of photon energy by one of the electrons which is shared cooperatively with the other electron through the Coulomb correlation; quantitatively it turns out to be one of the largest effects of electron - electron correlation known in atomic physics.