The distribution that best fits the statement where the probability of one element of the sample space is given by f(x) = 1/N, where N is the total number of whole values, is the Uniform Distribution.
In a Uniform Distribution, each value in the sample space has an equal probability of occurring. In this case, since the probability is defined as 1/N, where N represents the total number of whole values, it implies that each value has an equal chance of being selected.
Therefore, the Uniform Distribution is the most appropriate choice to represent the given statement.