Photon has a probability distribution of where it may appear if measured. Seems like photon itself chooses where to appear.
Not really, photon is not "choosing" to appear at some point over other. Quantum Mechanics is ultimately a model of reality, and a damn good one, in fact, the most accurate model of reality we have at present. However, it is not reality itself. Photon is simply following the laws of physics, which to us may forever be hidden, but we can still model their behaviour through probabilities, which is enough for all practical purposes.