When you concertedly think, the most pressing things rise to the top. That's it. There is no neural mechanism that 'picks' from an unlimited number of options. The mind is oriented to remind you of immediate issues, people, problems, etc. So when you decide to look at your thoughts, what comes up has a random component to it, but it will likely be some aspect of your immediate environment and life. So you *can* think about whatever, but you don't *decide* what you think, you just think about what comes to mind.
Consider this question: if you were to 'pick' something to think about, what is the substance you'd use to pick? How is this substance used to decide amongst various options? I'd argue, in actuality, what's relevant here is neural pathways and potentiation. Memories that have more relevance to our immediate life will be more prominent in our brain and more likely to be brought into our conscious awareness.
Often, our immediate environment is the spur to which memories we access, so we can act effectively in the real world. Sometimes, when we explore our own mind, concepts prompt certain paths.
Regardless, there's always a spur.
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How does a three year old, who lacks conscious awareness, exist in the world?
I can't find fault in any of that. When I tried to come up with something to think about, I'm sure there was a set of topics that floated into my mind based on any number of factors beyond my conscious control. And I'm sure the one I picked was picked behind the scenes before I consciously knew about it. But at least from my perspective, it usually FEELS like I can choose what to think about. I say usually because there are times when I can notice my behavior flowing from previous states (generally speaking; this also applies to the specific case of thoughts). It's certainly true that I can't choose what NOT to think about, which may be telling.
Not sure where you're going with your last question, but I would guess that a three year-old human exists in the world in much the same way a non-human animal does, given the same level of conscious awareness.
Was also thinking, it feels like you're choosing because in a sense you are choosing. I get the impression that some people get the sense that if we don't have control over our thoughts then we're just a ghost sitting in a machine that's acting for us. That's not the case either. Your mind rolling over thoughts, behaving, acting is you, which is why it feels like you're choosing, because this is what we are and how we work.
That method of living, though, just assumes that our 'freedom' is constrained by the content of our mind, and our abilities. We can not do that which we can not think.