Well, 70 years of 1/37 risk still has 13% chance of showing zero wars. Could happen. (Since we are talking about smaller ones rather than WWIII anthropics doesn't distort the probabilities measurably.)

One could buy a Pinker improvement scenario and yet be concerned about a heavy tail due to nuclear or bio warfare of existential importance. The median cases might decline and the rate of events go down, yet the tail get nastier.