I would suggest that when you see a "would" clause without an "if" clause, you should ask yourself whether it simply means that the speaker does not want to be so emphatic as to claim that this is the final and correct word on the matter.ex)...People from California would pronounce cot and caught in the same way...
"would" in if-clause conditionals means a certainty in a specific condition like "will".
For example, "If she came to the party tomorrow, I would be really glad". Doesn't this "would" still function as a certain "will" in an imaginary situation?
Yes, that's what a conditional is. It would happen if that situation existed. You can also say, "If she comes to the party tomorrow, I will be really glad." This is still conditional. If she doesn't come, you won't be glad.
But what I'm always confused about is if there's no if-clause like in ex)"People from California would pronounce cot and caught in the same way", does it mean a certainty on the condition as in "If there were the people from California, they would pronounce cot and caught in the same way" or low probability like "could" without if-clause?
No, I've explained that use of 'would' - more than once, I'm sure.
Many grammar books say "if clause" can be implied as a subject or an adverb phrase, so when I see sentences without if-clause, I try to think if the subject is a conditional-implying one or not. Okay, the summarized question is the following.
1. If you met Californians, they would pronounce cot and caught in the same way.(certainty = almost 100% if the condition is met)
Yes, that is one possible "if" clause. But it's arbitrary. The if clause is not defined, therefore you can't define it.
2. Californians would pronounce cot and caught in the same way. (certainty or low probability?? Is "Californians" an implied condition to replace if-clause? )
Do you mean, "If you were Californian, you would pronounce them that way"? No, it doesn't mean that, although that would logically follow.
3. You would see Californians pronounce cot and caught in the same way.(low probability??? without any condition?)
Yes, again this is implied by the original statement, but it's not what it means.