The drum spins => 2 out of 6 chances to land on a bullet.
It doesn't spin. There's an interesting consideration. Since the spot was empty, the next one can only be one bullet, as the second one is on the other side relative to the drum's rotation. We have 4 options for the empty spot that our predecessor hit, and only one is fatal for us.
Conclusion -- don't spin. That's what conditional probability says.
0.25<1/3. The cop correctly figured it out and explained it.