Note that "gonna" is very informal, and you should use "going to"... If you didn't know that, then you will have better luck searching now.

You know what would probably happen?

Right now if you dropped your coffee, it would spill. So if someone says, "(Do) You know what would probably happen?

The person you are speaking to knows you are talking about what would happen if you dropped the coffee.

You know what was probably gonna happen?

The second construction, though, is rare. Maybe you almost get caught smoking cigarettes, but you and your friend manage to sneak away. Then you might talk about what "was going to" happen. But the sentence clearly means that it no longer is likely to happen, because of the past tense "was". Something has changed since then.

Note that "gonna" is very informal, and you should use "going to"... If you didn't know that, then you will have better luck searching now.

Now, about sentence 3:

You know what would probably happen?

We can shorten "Do you know" to "You know", or even just "Know". That is probably what this sentence is doing - it's asking "Do you know what would probably happen?" You're right in thinking that "would probably" indicates conjecture here; a hypothetical situation. But would doesn't place the action in the past. You would use "have" for that - Do you know what probably would have happened?

(3) is about the future, in a sense; but it isn't really about time. it is saying that in general, if the condition that is being discussed is ever met, the speaker has a good guess at what the result would be (and he is announcing that he knows, and getting your attention.) You (the listener) could ignore the speaker, and he would tell you his guess. Or you could make eye contact to show you are paying attention, or you could ask "What?" Or, you might answer with your own guess:

Speaker: Ya know what would happen if you bought candy?
Listener: I would eat all of it.

It is not talking about the past; it is talking generally - it is just talking abstractly about a cause/effect relationship.

But this thing: You know what was probably gonna happen?

This construction is about the past. It is a pretty rare construction. I'll give an example use case for it -

Bob: Charles threw his ice cream in the trash!  What a waste.
Dave: You know what was probably gonna happen?
Bob: No, what?
Dave: It was probably going to drip on the carpet.

Because of the word "was", the sentence is speaking of the past. Whatever it was that was going to happen is no longer going to happen.

No, the would is not modifying time relationships. If it had "have", then it would:

You know what probably would have happened if I had fed the cat?

I think I drop the "had" sometimes in similar situations, but it might be a grammar error.

I'll take out the "have":

You know what would happen if I fed the cat?

Now we are talking about the future, you could say. We are using the continuous.

But it looks like you understand numbers 1 and 2

Note that "gonna" is very informal, and you should use "going to"... If you didn't know that, then you will have better luck searching now.

You know what would probably happen?

Right now if you dropped your coffee, it would spill. So if someone says, "(Do) You know what would probably happen?

The person you are speaking to knows you are talking about what would happen if you dropped the coffee.

You know what was probably gonna happen?

The second construction, though, is rare. Maybe you almost get caught smoking cigarettes, but you and your friend manage to sneak away. Then you might talk about what "was going to" happen. But the sentence clearly means that it no longer is likely to happen, because of the past tense "was". Something has changed since then.