I don't know in terms of the Uncertainty Principle, but the probabilistic behavior of unobserved photons (and electrons, and I think Helium atoms too, now) can be demonstrated with the two-slit experiment, where one photon is sent towards the slits, and the result of many photons being sent through individually over time results in an interference pattern. This is best explained by the photon interfering with itself. That is, the photon exists as a wave, and thus preserves the interference pattern of a wave, even though it is the only particle involved. However, if you determine which slit the photon traveled through, no interference pattern arises. You "collapse the photon's wave-function", and force it to act like a particle. Here's an explanation of the single particle behavior. I would imagine that there are some ways to deduce that the Uncertainty Principle is in effect for non-observed particles. Probably you could devise a scenario where the result observed could only be explained if the Uncertainty Principle were in effect.