How to measure Voltage without disturbing the circuit?
Older security systems use normally closed switches on doors and windows. They use a magnet and a reed switch to keep the circuit closed.

Then the circuit has a small amount current continuously flowing to monitor the circuit. The resistor is to limit the amount of current flow.

If the door or window is opened, then the alarm goes off. If a burglar cuts a wire, the alarm goes off. If the circuit gets jumpered and current goes higher then it either alarms or goes into trouble mode.

When you measure the voltage in operation and get 5v you are measuring the voltage drop on the resistor. When the circuit is open you are only measuring static voltage and it may not be very accurate.

So, in order to use the circuit without interfering with it, you need a high impedance voltage sensor in parallel with the resistor so it does not significantly increase current flow in the circuit. Then you will need a separate 3.3 volt supply, or take power from the Arduino board. The Arduino may not have enough power for your application so that is when you add an external power supply.

Building a voltage divider in the circuit is problematic as you have already found out.

Good luck!