I'll explain using smaller numbers.

Let's say you have ABCDEF, 6 letters.

The total number of combinations is 6!.

Now, A and B should be adjacent.

(AB)CDEF

Make as if A and B were stuck together; they form one item, for a total combination of 5!

But now, A and B could be either in the order AB or BA, so, you multiply by 2, the number of combinations with A and B together; 2 x 5!

Probability becomes

Sorry for my previous mistakes... it's 10 past midnight now, and I'm really tired. I'll answer tomorrow if there is still some unclear things.