  We provide a simple computation in order to estimate the probability of a
given hierarchy between two scales. In particular, we work in a model provided
with a gauge symmetry, with two scalar doublets. We start from a
scale-invariant classical Lagrangian, but by taking into account the
Coleman-Weinberg mechanism, we obtain masses for the gauge bosons and the
scalars. This approach typically provides a light (L) and a heavy (H) sector
related to the two different vacuum expectation values of the two scalars. We
compute the size of the hyper-volume of the parameter space of the model
associated with an interval of mass ratios between these two sectors. We define
the probability as proportional to this size and conclude that probabilities of
very large hierarchies are not negligible in the type of models studied in this
letter.
