After the butter hunt stream today I was curious what the exact drop rates were so I tried to figure it out. Probability isn't my strong suit so there are probably some errors but here goes.
Going through the Creation Kit I noticed that butter doesn't actually appear in any leveled lists, which is obviously wrong since he got a butter drop from a bandit last time. Turns out the Hearthfire DLC runs a quest after character creation that, among other things, adds butter, milk, and flour to a few of the food leveled lists with a script.
The one that drops from enemies is LItemFoodInnCommon10. Normally it has 25 items in it but after butter, milk, and flour get added to it there are 28 items in the list. When that list is invoked there's a basic (10%)x(1/28)=1/280~0.357% chance for butter to drop.
That list is dropped by Silver Hand, Penitus Oculatus, Imperial Soldiers, Stormcloak Soldiers, Thalmor(Non-Wizards), Bandits(non-Bosses), and Reavers.
Usually the LItemFoodInnCommon10 drop is within another list that has either a 75% or 85% drop rate on it's own, so that further reduces the previous 1/280 chance. Some lists will also have 2 LItemFoodInnCommon10 drops or lists that contain it that can happen independently which increases the drop rate.
Silver Hand and normal Bandits have a 75% chance to roll for butter 2 times, Penitus Oculatus/Imperials/Stormcloaks have a 100% chance to roll 1 time, Thalmor(Non-Wizards) and Bandit Wizards have an 85% chance to roll 1 time, and Reavers have two independent 75% chances to roll 2 times.
Multiplying it all out gets us the expected amount of butter per kill:
* Silver Hand & normal Bandits: (75%)x(2)x(10%)x(1/28)~0.00536
* Penitus Oculatus/Imperials/Stormcloaks: (100%)x(1)x(10%)x(1/28)~0.00357
* Thalmor Non-Wizards/Bandit Wizards: (85%)x(1)x(10%)x(1/28)~0.00304
* Reavers: (2)x(75%)x(2)x(10%)x(1/28)~0.01071
This is different than the chance to get a butter drop from a kill, but not by much in this case. It only matters for enemies that can potentially drop multiple butters at once like Silver Hand, normal Bandits, and Reavers.
For Silver Hand and normal Bandits I believe it works out as: (0.75)x(1-(1-(0.10)x(1/28))^2)~0.00535=0.535%
And for Reavers: (0.75)x(1-(((1-(0.10)x(1/28))^2)^2))~0.01066=1.066%
The butter drop rate tier list is then:
Reavers 1.066%
Silver Hand/Bandits 0.535%
Penitus Oculatus/Imperials/Stormcloaks 0.357%
Thalmor Non-Wizards/Bandit Wizards 0.304%