Sinewy Scourge
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Probability of Vindicare Killing Ahriman without rerolls
So the probabilities are as follows (with no reroll):
0 Damage = 42.1%
1 Damage = 05.6%
2 Damage = 11.6%
3 Damage = 15.4%
4 Damage = 11.9%
Kill = 13.2%
Now with a CP reroll
I'm working on the assumption that you use the reroll whenever you fail or when you roll a 1 or a 2 on the damage dice.
Splitting the probabilities for a reroll on the To Hit roll is easy we multiply all the outcomes by 1/6 (this is the probability distribution with a reroll) then copy all the probabilities for the successes, except that the 1/6 failure chance is already part of 0 damage so we subtract that from there.
For the reroll on the To Wound roll we can just repeat this process using the new To Hit Success from the previous calculation, as again the failure to wound is included in the 0 damage portion and the reroll can't be used if it already has been. In this case we subtract 5/36 instead of 1/6 as the entire computation is weighted as 5/6 of the whole, the other six being in the To Hit Reroll.
I'm assuming your opponent doesn't reroll the save, so skipping that part. Damage is a little more tricky as it changes weighting rather than the whole thing, in this case we need to rerun the calculation from my first post, but with the rerolls in place to shift the weighting. I've deducted 0 damage probabilities caused by failing to hit or wound and only left the 25/216 of a successful save in place, as the rest is accounted for in the To Hit and To Wound rerolls above. It's easiest at this point to also do the rerolls for the Headshot steps, so I'll combine that all below.
All we need do now is add all the results from the previous calculations together.
So the probabilities are as follows (with no reroll):
0 Damage = 42.1%
1 Damage = 05.6%
2 Damage = 11.6%
3 Damage = 15.4%
4 Damage = 11.9%
Kill = 13.2%
And with a reroll:
0 Damage = 22.8%
1 Damage = 03.9%
2 Damage = 09.4%
3 Damage = 16.5%
4 Damage = 18.1%
Kill = 29.3%
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Deffskullz desert scavengers
Thousand Sons 
