You have a capacitor and a switch.
When you close the switch the capacitor "samples" the input voltage.
When you open the switch, the charge has no place to go and so the capacitor "holds" this voltage.
Then the A/D converter may read this voltage at its own pace.
The key features are how well does the capacitor follow the input, it is a low pass filter after all, and how fast does the voltage leak off after the switch is opened.
Don't understand how you could do the experiment and lose the conclusion. I have confidence that according to the inscription on the silver chest:
"Who chooseth me shall get as much as he deserves,"