Think means a feeling based on some ideas, which is a thought comes from brain. What you “think” may be or may not be true.

Examples:

I don’t think it’s a good time to go outside. (may be it's good to go)

我覺得現在不适宜出去(可能出去是正确的)

Suppose is based on one’s thinking. To suppose that something is true means to think that it is true, but it may be false in fact.

Suppose something can be based on imagination.

Suppose is mostly used with first person pattern, for instance “I suppose you are right”, but it’s rarely to say, “She supposes you are right”.

Suppose基于一些證據的猜測(認為)。暗含着自己對對方所說的話信心不足，但自己目前無法證明對方是錯誤的。另外也有假設的意思。通常的用法是自己 suppose其他人。

Examples:

I suppose someone had to do it. (This is just what I guess. I may be wrong)

我猜有人要去做這件事(隻是表達猜測，沒有把握)

Suppose you are offered the job. Will you go? (Imagine the situation)

假如你拿到了這份工作，你會去嗎？

Presume means that it is based on your logical thinking, which has additional connotation of confidence, which commonly means that someone is confident of their assumption with some probability or evidences.

Someone who is "presume" something is more confident than someone who is "assume" something.

Presume是在有信心有證據的基礎上的假定。相比Assume, Presume給人傳達更多的信心。

Examples:

I would never presume it would be ok for people to hug the Queen.

我從來不認為我們可以擁抱女王。

Assume is to suppose something is true and will act as if it were true, but actually without proof.

Assume假設事實成立的意思，但事實上沒有證據能證明假設真的成立。

Examples:

I assume they will wait for us. (I don’t know it is a fact, but I will act as if it to be true)

我假定她們會等我們(我不知道真的會不會，但我以她們會等作為前提)

I assumed that you had known the result. (no evidence, just based on my personal guess)

我假定你已經知道了結果(雖然我沒證據，但我後續所有的行為都基于此假定)

In general,

Suppose implies some doubt about an assumption.

Assume has neutral(中性的) connotations(暗示).

Presume has roughly opposite(相反的) connotations (confidence) compare with “Suppose”.

Examples:

I suppose it is safe to assume that the trains will resume services on Monday, but we can still think of other modes of transport like flight or bus as another option.

我覺得比較靠譜下周一鐵路交通服務會恢複。但我們仍然可以考慮其他的交通方式作為備選項。