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.