If Prejudice is defined as Preconceived opinion not based on reason or experience. then what, if any, is the word that defines "Preconceived opinions that are based on experience or reason?"
Anecdotal: Evidence or beliefs based on what has happened to someone personally.
(definition typically says in the form of stories that people tell - but the main point is the notion is not based on any empirical or scientific evidence).
"His conclusions are not supported by data; they are based only on anecdotal evidence."
An opinion is a conclusion reached that is not factually determined. Oxford offers these two definitions
a view or judgement formed about something, not necessarily based on fact or knowledge: that, in my opinion, is right
a statement of advice by an expert on a professional matter: if in doubt, get a second opinion
In both cases, the result of the analysis is not an exact calculus of indisputable facts, but requires some measure of decision-making by the opinion holder.
Obviously, there is a wide spectrum in the quantity and quality of information that leads to the opinion, ranging from none to a wealth of data and experience by an expert in the field.
The definition of preconceived is
(of an idea or opinion) formed before having the evidence for its truth or usefulness: the same set of facts can be tailored to fit any preconceived belief
The phrase preconceived opinions that are based on experience or reason seems somewhat oxymoronic. If it is preconceived, the suggestion is that it lacks evidence (experience being a form of evidence and reason the analysis of that evidence).
If facts are indisputable, the conclusion is not an opinion. If there is some room for differing opinions, it's because all the facts are not, or cannot be known, and some prejudgment (before all facts are know) is necessary.
It seems as if you are describing a circumstance where some facts are known and the opinion holder has experience and reason on her side. Rather than describing it as preconceived, you may want
I think you are referring to bias.
3a : bent, tendency b : an inclination of temperament or outlook;
although this definition refers also to "prejudice."
A single word for a preconceived opinion that could be based on reason or experience is prejudgment. However, there is no single word for prejudgment based on reason or experience. The two-word phrase experiential prejudice is problematic because although literally, the word prejudice derives from prejudgment, the words do not mean the same thing: modern dictionary definitions of prejudice require that the opinion not be based on experience or reason.
If one has lived long enough, opinions can resemble hunches. The evidence I've read indicates that these hunches are the result of subconscious recollection of varied past experiences, filtered by the brain to give direction in times of conscious uncertainty.
Those who have religion in their life believe these hunches to be signals from a deity.