The probability theory around a candy bag

The question you are asking here is the classical question of inferential statistics: "Given the outcome of an experiment, what can be said about the underlying probability distribution?"

You could, for example, give an estimator for the unknown quantity "number of caramels" (called $a$ from here on). The one most often used (since its easy to calculate) would be the maximum likelyhood estimator, where you estimate $a$ to the the value that maximizes the probability of the outcome.

In this case, you'd choose $a$ to maximize $P_a(7)$ (the probability of drawing the first caramel in the seventh draw, assuming there are $a$ of them). A little Excel calculation, along with Isaac's way to calculate $P_a(7)$ results in $a$ to be estimated as 14.

To judge, what this result is worth, you'd need to calculate the mean squared error of this estimator, which is not as easily done.

If you already had a hypothesis about $a$ (say $a$ < 20), you could use your experimental result to test it, using statistical hypothesis testing, too.