Actually, it is because of the major difference between the size of the resistors. As it is really big, there's almost zero current flowing on the line with the biggest resistor. There is a minor change in the voltage, but it is really small, so your Arduino can't even detect it. Unfortunately, this feature cannot be used, this is a mistake in your book. If you want to go sure, apply Ohm's Law, calculate the currents, and you'll see the reason.
Sorry for bad English, I'm not a native and really unfamiliar with topic-specific vocab.
I hope, I could help.
Sokosz