How do you know when your kid is lying?

Tungsten likes to chew gum.

I keep packs in my office and she frequently comes down to ask for a piece.

Since she woke me up at 4am today, when we went to do pull-ups (or I did at least), I didn't feel like I wanted to reward that behavior.

I told her she couldn't take a piece of gum.

A few minutes later, I saw a piece in her hand.

I asked her where it was from.

Everything about her demeanor suggested I had caught her. She told me a story about "taking it from the drawer upstairs."

Her story was plausible, but with only about a 1% chance of likelihood.

I wanted to believe her.

How do make it so that they only tell you the truth? Impossible?