To express a possibility of something happening (supposition), expressions in English that show possibility (I guess, I think, It must, It seems, etc.) are almost interchangeable. Just like English, Korean also has a lot of ways to express supposition. However, from what I understood, they are not quite interchangeable.--- that's why it took me time (and it still is) to grasp the differences. I decided to share my conclusions with y'all. And by all means, this is just MY conclusion. I'm pretty sure there will be a lot to correct, that's why I'm opening a discussion so we can all correct and help each other out.
(ALL INFORMATION IS BASED ON WHAT I WAS TOLD)
1. -겠다
This ending is also used for future tense conjugation. But it is usually used as "-겠습니다" which is the formal form of future tense.
I usually hear this verb ending in words like 맛있겠다 or 재미겠다. If you use a translator, these expressions translate to "Looks delicous" and "Sounds fun." But the literal meanings are "It must be delicious" or "It must be fun."
In other words, -겠다 can be translated as "It must be..."
However, it is not used the same way in Korean as you would in English. Based on what I was told, -겠다 gives off a high-certainty of something happening. And you usually conjugate a verb to this form as a response to a given situation or information at THE VERY MOMENT.
Ex.
Your friend tells you she is going to England. You can say 재미겠다 as a response. (information given at the very moment)
You just arrived in the Bahamas. You can say 재미겠다 to express certainty that the trip will be fun (situation given at the very moment). However, if you are just packing for the Bahamas, you cannot say 재미겠다 to express that the trip will be fun BECAUSE the trip is not starting at that moment.
2. -을/ㄹ 것(을) 같다
It translates to "I think (it wil)..."
This is the softer version of -겠다
It is also a softer version of the normal future tense conjugation.
In other words, the situation doesn't have to be present at the very moment when you use this conjugation.
Ex.
You are packing for the Bahamas, you can say 재미있을 것 같아요 (I think it will be fun.)- softer version of future tense
You arrived in the Bahamas, you can also say 재미있을 것 같아요 . -softer version of 재미겠
3. 을/ㄹ 수도 있다
It translates to "It might..."
You use this to express a contrary opinion to a situation.
For example,
Your friend tells you that the restaurant you want to go to is terrible, yet you STILL BELIEVE that it's good because your parents told you it is.
You can say 좋을 수도 있어. -- you are emphasizing that although your friend says it's bad, you still want to try it because "It might be good" (you are holding on to your belief that the restaurant is a good/decent place to eat)
I was also told that it is odd to say this expression without stating the reason that led to your belief, unless it's too obvious.
Example (in English)
Just saying "I might not be able to go" to a party your friend invited you to IS ODD.
You should say "I have a tight schedule, so I might not be able to go" instead.
4. -는/ㄴ가 보다
Translates to "I guess..."
You basically use this to emphasize your opinion on something that happened/ is happening (and there is evidence). (Although it does not express possibility of something happening, it still expresses POSSIBILITY).
Example:
You see your brother eating his food excitedly. You can say 맛있는가 봐 ( I guess it's good/ I suppose it's good)--- you are emphasizing your opinion of the food being good because you see you see how your brother eats it; there's evidence.
And that's all I know. Please correct me if I'm wrong. Or add information that you think is important.
It is very common for “~는/ㄴ가 보다” to be shortened to “~나 보다”
Refer to https://www.howtostudykorean.com/unit-5/lessons-109-116/lesson-109/