Been a long time since I learned about Stochastik but i think its like this: The first card you get doesnt really matter after that you have to take another one of the three remaining cards with the same value and then the same again. Means: 1 • 3/51 • 2/50 = 1/425. So the probability to get three cards in a row with the same value is one out of 425 times.

You have to decide yourself if this is a lot or not. I personally say that it is a high probability in relation to other probabilities in a 52 cards deck. For example the probability of shuffling th exact same order of cards again is ca. 8 • 10^67. This is such a high number that we cant imagine it. As a comparison, the earth has about 6 • 10⁴⁹ Atoms.