Set your difficulty level to hard and a villager will always be infected.
On 'normal' the chances are 50%.
On easy the villager will always be killed.
Lol. I have to admit I feel just a tiny bit stupid now.
Of course I know about the golden apples, and had them ready to administer - but I didn't, because
a - the splash potion did not seem to have any effect, and
b - them apples are so expensive and precious, I thought I would be wasting them if applied right away.
So, thanks to your comment, I gave myself a push, threw another splash potion and fed the apple right after. The good man shuddered, and soon after was cured!
I still don't get the grey and red particles the zombie villager is supposed to be emitting, but I'm almost certain this is because of my video settings in the options menu (haven't yet checked).
I have 5 zombie villagers, each one blocked in separately, and a block above their head for sun protection. When I throw a splash potion of weakness at them nothing happens - no grey particles emitted from the ZV....
The splash potion is definitely working though, because if I stand too close the effect shows up on myself.
What could I be doing wrong?