Scotty's Car Between Vacant Spots

Scotty parks his car in a row of $N = 15$ spots. He never parks at either endpoint -- his car is always somewhere in the interior. He then leaves, and when he returns, he finds that $k = 6$ total cars are in the lot (including his own), with the other $5$ having parked uniformly at random among the remaining open spots (at most one car per spot). What is the probability that Scotty's car has an empty spot on both its left and its right? Round to the nearest thousandth.