Apply the following expression to a 3D layer’s Opacity property:

  startFade = 500; // Start fade 500 pixels from camera.
  endFade = 1500;  // End fade 1500 pixels from camera.
  try{ // Check whether there's a camera.
      C = thisComp.activeCamera.toWorld([0,0,0]);
  }catch(err){ // No camera, so assume 50mm.
      w = thisComp.width * thisComp.pixelAspect;
      z = (w/2)/Math.tan(degreesToRadians(19.799));
      C = [0,0,-z];
  }
  P = toWorld(anchorPoint);
  d = length(C,P);
  linear(d,startFade,endFade,100,0)

The fade starts at a distance of 500 pixels from the camera and is complete at 1500 pixels from the camera. The linear interpolation method is used to map distance values to opacity values.