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My reading is the Buddha said the King had the capacity for awakening but the King's mind was still emotionally hindered by the action of killing his father.
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Even "determinism" is based on conditions. If a student's about to take a very tough rigorous final exam, if s/he doesn't spend enough time and effort to study up, on the day of the exam, it's "deterministic" that s/he will fail the exam. Similarly, the Five Heinous Offenses are a class of offenses so grave that once committed, it's deterministic that one's next life will be in woeful states, even after one tried to make up for it with wholesome deeds later on. That doesn't mean those good deeds are for nothing, but it does mean that their fruition will have to wait for the fruition of the heinous offenses to manifest first. That pretty much was the case of prince Ajatasattu in the DN sutta.
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I think it mean he would have definitely attain stream entry after listening to the Buddha’s teachings if he didn’t kill his father.
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I think the Buddha does (supernaturally) know the condition[s] in which someone might become enlightened.
Like (I don't know if this is a good example) this isn't "deterministic" but I know that "if I hit something with a hammer then it will break".
A more explicit story like that is, for example, The Weaver's Daughter from the Dhammapada commentary:
Now one day, as the Teacher surveyed the world at early dawn, he perceived that this maiden had entered the net of his knowledge. When he saw her, he considered within himself, "What will happen?" And he became aware of the following, "From the day when this maiden heard my discourse on the Dhamma, she has practiced meditation on death for three years. I will now go to Alavi and ask this maiden four questions. On each of the four points she will answer me correctly, and I will congratulate her. I will then pronounce the stanza, This world is indeed blind. At the conclusion of the stanza she will be established in the fruit of stream-entry. By reason of her, my discourse will be profitable to the multitude besides." So the Teacher, with his retinue of five hundred monks, departed from Jetavana, and in due course arrived at the Aggalava monastery.
I'm pretty sure there are other examples of stories like that in the suttas.
I think that's part of what makes the Buddha "a Buddha" -- i.e. insight into other people so as to know how best to teach them.