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The chaotic nature of the atmospheric dynamics has stimulated the inclusions of methods and ideas derived from statistical dynamics. For instance, weather predictions have recently been based on the development of extensive ensemble systems that are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts allowing forecasters to issue probability-based forecasts. These works have modified the dominant paradigm of interpretation of the evolution of atmospheric flows (and to some extent also of oceanic motions) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, that turns out to be the only physically meaningful quantity, but little work has been done on a direct modeling of the probability evolution itself. In this paper we show that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows to obtain a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and it provides a framework generalizable to red noise, lagged equations and even field equations, i.e. partial differential equations with noise. These concepts will be applied to an example taken from a simple model of ENSO.