Brainteaser - Alex's Fish

Alex Atala is preparing a Peacock Bass (Tucunare) of length \(L\) for dinner. He selects two cutting points uniformly at random and independently along the length of the fish so that the cutting points are on opposite sides of the midpoint of the fish. What is the probability that the distance between the two points Alex selects is greater than \(\frac{L}{3}\)?