The one-dimensional conformal model and the three-dimensional model for phase-resolving numerical simulation of sea waves were used for investigation of a freak wave nature. The calculations with conformal model were done for 7120 peak wave periods. The small subgrid dissipation of energy was compensated by integral input of energy, so, the energy was preserved with the accuracy of 4 decimal digits. The probability of the trough-to-crest wave height, crest wave height and trough depth were calculated. The uncertainty (dispersion) of the calculated probability is demonstrated. It is confirmed that trough-to-crest height equal to 2, approximately corresponds to the crest height equal to 1.2. Freak waves appear randomly in a form of the groups separated with large intervals of time. The hypothesis that freak wave can appear as a superposition of modes gathering in the vicinity of a dominant wave crest turned out to be incorrect. It was proved by a special phase analysis with the conformal model and 2D-model that the height of wave does not correlate with the phase concentration (expressed as a sum of crest heights of modes in the vicinity of crest of the main mode). The probability of large waves is monotonic over the wave height. It allows us to suggest that large waves are an indigenous property of a random wave field, and they are typical though quite rare events. The spectral image of wave field with a small number of modes can indicate the presence of freak waves, but this effect disappears completely when the length of such wave is much smaller than the size of domain. The Fourier approximation of freak wave in such domain requires many spectral modes in the same way as the approximation of pulse function. The abnormal growth of wave height looks rather like the self-focusing of single wave involving concentration of energy in the vicinity of wave peak. The breathers most closely correspond to the nature of freak waves.