Now, I know you probably want an official source answer for this question, so feel free to hide this if you don’t think this is an acceptable answer.
However, I really doubt we will officially be told the exact chance, since we haven't already, and so I have decided to devise and experiment to answer this question.
I looked around for Pokémon that appear in hordes that I could easily determine whether or not they had their hidden ability. In the end I settled on the Whismur hordes in Connecting Cave for this experiment.
I chose Whismur for several reasons. Firstly, they are common, meaning I won’t be spending half an hour to get just one horde. Secondly, they have Soundproof as their only regular ability, and Rattled as their hidden ability. If you are thinking “how the heck do you easily test for Rattled?”, then my response is I didn’t need to. Since Soundproof is their only regular ability, those without Soundproof must therefore have Rattled. While Rattled may take some time to test for, Soundproof is very easy to test for. Simply have your Pokémon use Growl, and a message will flash up telling you how many have Soundproof. Since Growl affects every opponent, it means I only have to use it once to tell how many have Soundproof, and how many have Rattled.
My Growl user was my trusty Kricketune. Why? Well, that is mainly because Kricketune was the highest levelled Pokémon I had in my box that still knew Growl, which is generally considered rather useless.
I ended up testing 200 Whismur hordes, which gives a total of 1,000 individual Whismur.
So now I have established my methods, what were my results? Well, 952 Whismur had the ability Soundproof and 48 had Rattled. Since I am only interested in the Hidden Ability for this, then 48/1000 = 0.048 or 4.8%
The Final Answer:
So from this experiment I got the chance of a Pokémon in a Horde with its Hidden Ability is 4.8%. Since GameFreak seems to like round numbers, I suggest the actual answer is probably 5% then.
If anyone else wants to try this experiment (either with Whismur, or another horde of your choice), then compare your results to mine and see what you get. Since this is statistics, the more people who actually do an experiment like this, then the more accurate our answer will actually be.