Okay so arrangements of items where the order matters are called permutations. That is to say, if you consider ABC, ACB, and BAC to be different, they are permutations. Anyway, this comes from two assumptions. The first is that Arena will never offer you two of the same card at any given time (Meaning you won't have to pick between three wisps). The second is that every common has an equal chance of being selected. Now the second one is actually false from my understanding, as IIRC class cards have a higher chance than neutrals, but for the purposes of calculation this assumption will have to do or it will get way too complicated. Just take this with a grain of salt since arena drafts are more complicated than a purely random selection. Anyway, from the hearthstone wiki I found that there are 374 common/basic cards in Hearthstone.
The way to calculate the number of permutations of r objects from a set of n objects is
n!/(n-r)!
Where ! denotes a factorial (which mulitplies up every natural number before it. That means 4! =1×2×3×4 and so on.). Anyway, our n= 374 and our r=3. Now if you try to put "374!" Into your calculator you'll almost certainly find that the number is too big and your calculator can't handle it. However, we can use a trick to find the permutations. Recall that n! = 1×2×3×4...×(n-1)×n, and that (n-r)! = 1×2×3×4...×(n-r-1)×(n-r). You'll notice that the vast majority of the terms are the same, and so they cancel out when dividing. So, we end up with only the last r terms of n!. In our case, it's the last 3 terms of 374!, which would be
372×373×374 =58, 894,744.
A pretty big number. That means that thr chance to get any single permutation of commons in Arena is 1/58,894,744 , or ~0.000 002%. Now, this seems impressive. But that's only for one time, and you get a chance like this with every single common selection in Arena. To get the probability of the same one twice, I'll assume the same probability. This is incorrect since Arena has a chance to give you non-commons and again it's not purely random. Regardless, it's just a ballpark. This means you have to square the chance of it happening once. This ends up with like 0.000 000 000 000 04% chance.
Again because I know people will not read the post and try to correct me on this saying dumb shit like "Arena isn't purely random!" And dumb shit I will put a disclaimer at the bottom.