Leading Digits in Hexadecimal
A large dataset of positive quantities spans many orders of magnitude and obeys Benford's law in every base: in base $b$ the leading digit $d \in \{1,\dots,b-1\}$ occurs with probability $\log_b(1 + 1/d)$. The values are written in hexadecimal (base 16). What is the probability that the leading hexadecimal digit is 1, 2 or 3? Give your answer as a reduced fraction.
Related problems
Source: Benford's law in a general base b, a standard generalization; T. P. Hill (1995) showed that base-invariance characterizes the law. Statement written for AxiomIQ.