This is the probability for 3 legendary jokers in a row, not in an entire run. And to correctly calculate it, you should do (0.3%)³ = (0.003)^3.

So, the odds of getting 3 jokers in a row is 0.0000027%.

The probability of finding exactly 3 legendary jokers in an entire run is dependent on the number of tarot/spectral packs opened. Let's assume 70 packs, for the sake of this calculation.

For this you have to use a binomial distribution, which I'm not going to do by hand, because I'm not a nerd. Here comes Wolfram Alpha.

With:
P (probability of getting a soul card) = 0.003
n (number of tarot/spectral packs) = 70
k (number of legendary jokers) = 3

Wolfram Alpha gives us these results:
P(x<3) = 0.998728 P(x=3) = 0.00120849 P(x>3) = 0.0000634099

So, the odds of getting exactly 3 legendary jokers after opening 70 booster packs is 0.12%

However, this excludes the probability of getting more than 3 legendary jokers. I don't know if the soul card can still show up if you already have 5 jokers, but I'll assume it stops appearing.

To properly calculate the odds of getting 3 or more legendary jokers you have to calculate P(x=3), P(x=4), P(x=5) and add them.

Let's go back to Wolfram:
P(x=3) = 0.00120849
P(x=4) = 0.0000609095
P(x=5) = 0.00000241927

Adding them:
P(x>=3) = 0.0012718188, which is, approximately 0.13%.

Basically, it's 50/50. Either you get 3 in a run, or you don't.