I would suggest that the behaviour of the gazelles you are citing is perhaps over simplified. There will likely be temporal and spatial dynamics in their behaviour... Prey will probably spend more time concentrating on observation when they know there are predators around. There will also be likely peak times during which hunting occurs (in savannah systems it tends to be dawn and dusk) and prey would be more cautious at these times.
It seems to me that the prey would not be judging the hunger of the predators but instead they learn the consistent patterns in the level of risk associated with being near predators. This could be genetic in its cause. If there is a gene (or genes) which determine when a prey individual is most likely to be out in the open grazing then the higher probability of predation at certain times would reduce the frequency of the genes which cause that choice.
There could also be fluctuations over time as the predators learn that the prey have become less cautious, which then causes predators to take advantage of unsuspecting prey, which you might be interpreting as the "faking" behaviour... it is not a deliberate fake, more taking advantage of the risk taking behaviour of the prey (as time passes without attack they will become more brazen). To the best of my knowledge there are no examples of the deliberate fake but predator prey dynamics are not my specialism.
Overall, I think you are asking a question based on learning and information use of repetitive patterns in behaviour of predators by prey, and have interpreted these behaviours in an over complex way (see Occams Razor).