1. A driving assistance system provided in a vehicle that a driver operates, the system comprising: a detection unit that detects a distribution of a driver's gaze; an ideal computation unit that computes an ideal probability distribution of a driver's gaze, from the distributions detected in a past and information, wherein the information is derived from the vehicle and a periphery surrounding the vehicle, the ideal computation unit including an imaging unit that obtains image information ahead of the vehicle: a visual-field-image accumulation unit that accumulates image information corresponding to a driver's visual-field from the obtained image information and the detected distributions; a first computation unit that computes a probability distribution of a driver's gaze required for steering operation for traveling a road after obtaining a shape of the road from the accumulated image information, to thereby output a first result; a second computation unit that computes a probability distribution of a driver's gaze expected from a visual characteristic of the accumulated image information, to thereby output a second result; and an addition unit that adds up the outputted first result and the outputted second result to thereby obtain the ideal gaze probability distribution; a risk determination unit that determines presence of a risk when a difference between the detected distribution and the computed ideal probability distribution exceeds a given threshold; and an output unit that outputs a result determined by the risk determination unit.