Exactly this phenomenon is used in [beam splitters][1]. A beam splitter is normally designed to have a 50% chance of reflection and a 50% chance of reflection, while your glass block will (probably) not have equal reflection and transmission probabilities. However the basic principle is the same.

Incidentally there is a related question at http://physics.stackexchange.com/questions/66498/what-happens-when-a-photon-hits-a-beamsplitter and you may be interested to read the answers to that question.

The answer is that when the photon reaches your glass slab it will form a superposition of the reflected and transmitted states. So the photon is **both** reflected and transmitted. If we interact with the system to perform a measurement we will collapse the superposition and we'll find out whether the photon was reflected or transmitted. However there is no way to tell in advance what the result will be. The best we can do is calculate the probabilities that the measurement will find the photon in the two states.


  [1]: https://en.wikipedia.org/wiki/Beam_splitter