Determine $P(X > n +k\mid X > n)$ 
Bob is at the shooting range. 
  With probability $\frac{1}{3}$ Bob hits the target. 
  Every shot is independent of the previous ones. 
  Bob starts and keeps shooting until he hits the target. 
  Let the random variable $X$ be the number of the shot that first hits the target. 
  For integers $n$ and $k$, determine $P(X > n +k\mid X > n)$.

I start working on the conditional probability that becomes: $P(X > n +k\mid X > n)=\frac{P(X > n + k\:\cap\:X > n)}{P(X > n)}=\frac{P(X > n+ k)}{P(X > n)}$ 
Now how can I compute the probabilities from the data that I know, which distribution should I use, or how can I use the probabilities given in the question?

The probability of Bob not hitting the target is $2/3$, so the probability that he misses $x$ times is $(2/3)^x$, since the individual shots are independent. How could you express the statement "Bob misses the target $n$ times" symbolically?
