There are a few mistakes.
Your intention is to measure the potentiometer wiper voltage. You've connected the wiper to A0, which is correct. But then it seems that you were tempted to close that circuit by connecting A0 to ground. Doing so is misguided: that will just short that entire branch of the circuit to 0V. You don't need to close that circuit because you want to peek at the wiper voltage, not draw any current from it.
As a matter of fact a very tiny amount of current will be drawn from A0, through the ADC, and back to ground. This is an undesired side-effect of the circuit the ADC uses to measure the voltage. ADC designers do their best to keep this very small, in the order of micro or nano amps, because that current could modify the voltage you're trying to measure.
For the same reason you can't measure the voltage "through" the LED to see it working, because almost no current should flow through that branch, so it would not turn on. It would also modify the voltage you measure.