What Greene is saying is that these three different planes of simultaneity are equivalent to slicing a loaf of bread at three different angles.
[Apparently he never worked in a real world bakery. You can't slice bread that hasn't been baked. The block universe is a nonsensical idea, that does not consider new events. and the act of perception. An event occurs once and is perceived multiple times.
An event E happens, and the light is dispersed throughout the universe. Since all observers, known and unknown are at varying distances, they will perceive E at varying times, depending on their motion relative to the location of E. For those who have detected the image of E, it's history. For those who are processing the image, it's 'now'. For those who haven't detected an image, it's a probability. Perception of an event now is not perception of another persons future. The most it can be is a common event in their histories.
The temporal location of an event is relative to the observer, in keeping with 'time is observer dependent'. Considering the vast astronomical distances, Earth only intercepts a tiny pencil of light from any distant source, thus most events pass us by. Locally, we never see the far side of the moon.
A perception by A does not guarantee a perception by B who is more distant from the original event. Prediction is based on prior knowledge and has a probability value. B might be sleeping when the image arrives, the weather could interfere, or B could die before the image arrives.
I have a can of tomato sauce, intended for a pasta recipe. Nobody will see the sauce pour from the can before I do, and not until I open it. The event underlined does not exist yet.
B. Greene also likes metaphors like 'moving in time'.
If the future is fixed or predetermined, then law enforcement becomes ineffective. The criminal defense is ' it was meant to be'.]