I've found this Log5 approach which seems to be good enough for me.
It estimates the probability of A defeating B via the following formula:
$p_{A,B} = \frac{p_A-p_A\times p_B}{p_A+p_B-2\times p_A\times p_B}$
$60\%$ and $30\%$ become $77.(7)\%$ and $22.(2)\%$ which fits my expectations quite nicely.