Benford's law
Randomly choose a number from a frequency distribution.
How likely the number's leading digit is $d$ (in a base-$b$ numeral system)?
$$
p(d)=
\begin{cases}
\log_b \big(1+\frac{1}{d}\big), & \text{if $d = 1, 2, \cdots, b-1$,} \\
0, & \text{otherwise.}
\end{cases}
$$