Small dice total given two or more even faces

You throw three fair six-sided dice. Knowing that two or more of them came up even, find the probability that the three values add up to at most $7$.

$13/108$. Mapping each die $x\mapsto7-x$ swaps parity, so exactly half of the $216$ outcomes, $108$, have at least two even faces. Among those, the ones with total at most $7$ are permutations of $(1,2,4)$, $(1,2,2)$, $(2,2,3)$ and $(2,2,2)$: $6+3+3+1=13$.