Someone might want to check my math and reasoning on this, but I think this can be calculated using a binomial distribution.
A binomial distribution is used to calculate the probability of observing a certain amount of successes given a certain amount of trials.
So in this case, we have 5 slots in the shop, and we want 3 of them to be Leona.
Next, we need to calculate the probability of hitting a Leona. This is the part where I'm not confident on my math.
I assume that no 5* units have been taken out of the shop. In Set 8, there are 8 different 5* units and there are 10 copies of each of them. A total of 80 copies if nothing has been taken out. 10 of which are Leona, which means 10/80 = 1/8 is our chance of hitting a Leona specifically.
I believe the way the calculation works is that for each of the 5 slots, the game rolls a dice and 4% of the time (at level 8 shop odds), any one slot will offer a 5. That means the odds of each slot to hit a Leona specifically is going to be 4% (the odds of hitting a 5) multiplied by 1/8 (the odds of the 5* being Leona instead of one of the other 7 5* units) which is about 0.5% or 1/200.
Now we have all the information we need to calculate the probability.
x = number of successful attempts = 3
n = number of attempts = 5
p = probability of each attempt being successful = .5%
So, if we plug into the equation for a binomial distribution (which is too long to type up, just Google if you're curious) we get a probability of about 0.0001238%. So that means seeing 3 Leona's in a single shop at level 8 would happen in about 1 in every 10,000 rolls.
This isn't just true for Leona, this is true for any specific 5* assuming none have been taken out of the pool. You can redo this math for any situation by recalculating the probability.
p = probability of each attempt being successful = (probability of level shop odds) * (number of unit you want in the pool / total number of units at that rarity in the pool)
You can also calculate this for more than exactly 3 copies as well. If you want AT LEAST 3 copies in the shop, then you just have to redo this calculation for x = 3, x= 4, and x = 5 and add them all together.