Ok, what's happening is that your Kenko TC isn't recognised by your camera. The pins are there to just carry the information from the lens to the camera. So, the camera sees a 70-200mm f/4 lens when in reality the TC would multiply both your focal length and your aperture by twofold. That's why you still have the f/4-f/8 as options and you maintain AF. If you were using a Canon TC, this has full communication with the camera, so your camera would recognise it giving precise readings of the lens+TC combo, giving you correct EXIF and correct aperture readings. You would also lose AF because all cameras except from the 1 series lose AF with apertures smaller than f/5.6. But since your metering is done in the camera and not in the lens, by choosing f/4 the camera would meter the scene as it sees it. But it's a lot darker than f/4 because it's actually f/8 so it compensates for that, even though it thinks that it's f/4.
The aperture is the size of the diaphragm in relation to your focal length. So for your 70-200mm f/4, the size of the diaphragm at 200mm is 200/4 = 50mm. The aperture blades are in the lens, not in the teleconverter, so the actual size of the diaphragm rermains the same, right? As I said before, the aperture is just the relation between your focal length and the size of the diaphragm. So if the teleconverter increases your focal length to 400mm, then your aperture would be (here's some simple maths)
400/x = 50
400/50 = x
x = 8
So your aperture is f/8. It's that simple!