Honey detector

I’ve stumbled upon a collection of infinitely large honeycombs, as pictured below. Each honeycomb has at most one source cell (X), from which the honey flows down the honeycomb. While I cannot look into the honeycomb, I have fortunately have a machine to check for honey.

The machine chooses a random cell (with uniform probability) and simply checks whether the cell contains honey. Assuming one-third of honeycombs contain honey, what are the answers to the following questions?

If a honeycomb contains honey, what is the probability of detecting it? If no honey is detected, what is the certainty that there is no honey in the honeycomb?

Please send your name and answer with the title [HONEY-ANSWER] to puzzle.tangier@gmail.com.