Let $x$ be chosen at random from the interval $(0,1)$. What is the probability that
$\lfloor\log_{10}4x\rfloor - \lfloor\log_{10}x\rfloor = 0$?
Here $\lfloor x\rfloor$ denotes the greatest integer that is less than or equal to $x$.

$\mathrm{(A)}\ \frac 18 \qquad \mathrm{(B)}\ \frac 3{20} \qquad \mathrm{(C)}\ \frac 16 \qquad \mathrm{(D)}\ \frac 15  \qquad \mathrm{(E)}\ \frac 14$