  We outline some simple prescriptions to define a distribution on the set
$\mathbb{Q}_0$ of all the rational numbers in $[0,1]$, and we then explore both
a few properties of these distributions, and the possibility of making these
rational numbers asymptotically equiprobable in a suitable sense. In particular
it will be shown that in the said limit -- albeit no uniform distribution can
be properly defined on $\mathbb{Q}_0$ -- the probability allotted to a single
$q\in\mathbb{Q}_0$ asymptotically vanishes, while that of the subset of
$\mathbb{Q}_0$ falling in an interval $[a,b]$ goes to $b-a$. We finally give
some hints to completely sequencing without repetitions the numbers in
$\mathbb{Q}_0$ as a prerequisite to the laying down of more distributions on it
