Shuffling Cards Probability Question

[saculnoogal]

So I like to shuffle a deck of cards and go through it looking to see if there are any of the same number card in a row so like the 4 of clubs next to the 4 of diamonds for example. Most of the time there is at least one pair (Two of the same number card in a row) when randomly shuffled. Getting a triple (3 Of the same number cards in a row) is more rare but happens from time to time. I happened to get all 4 4s in a row the other day while shuffling and I was wondering what the odds of that are because i've shuffled many times and this has never happened to me. Thank you!
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[Romsek]

pick a slot for the 4 of them. There are 49 of them.
arrange the 4s in the slot. There are 4! = 24 ways to do that.
the rest of the 48 cards can appear in any order. There are 48! ways to do that.

So there are [MATH]49\cdot 24 \cdot 48![/MATH] ways that 4 sequential 4's can appear in the shuffled deck.

There are $\displaystyle 52!$ ways that the deck can be shuffled.

[MATH]p = \dfrac{1176 \cdot 48!}{52!} = \dfrac{1176}{52\cdot 51\cdot 50 \cdot 49} =\dfrac{1}{5525}[/MATH]
Pretty uncommon but not impossibly so.