We use the formalism of Volterra series as a tool of probabilities in order to assess the risk's level in those far coast Peruvian cities under a potential risk to the affected due to imminent arrival of climate phenomena such as El Niño that have seriously affected populations located along the Peruvian coast from past decades having been the most recent impact on the 2017 summer. Essentially we follow the methodology given by: (i) we propose the Volterra formalism, (ii) we test the most suitable probability distribution, and (iii) we adjudicate a physical meaning to the resulting output. For this end we establish that the input function is related to distances to be in risk by flooding in urban areas. Our proposal of perceiving a Volterra-based probability theory is founded on the basis that the input probability distribution functions are convoluted together to their Volterra kernel that in this analysis are denoted by orthogonal polynomials. We apply this formalism to assess risk in Urban areas located along the far north cities in Perú. Our approach has turned out to be validated as to identify those zones of risk inside the main urban zone of the Tumbes city. The identified zones corresponding to those areas that might be characterized by being very sensitive to the flooding.