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)
我觉得现在不适宜出去(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基于一些证据的猜测(认为)。暗含着自己对对方所说的话信心不足，但自己目前无法证明对方是错误的。另外也有假设的意思。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)
我猜有人要去做这件事(只是表达猜测，没有把握)
Suppose you are offered the job. Will you go? (Imagine the situation)
假如你拿到了这份工作，你会去吗？
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是在有信心有证据的基础上的假定。相比Assume, Presume给人传达更多的信心。
Examples:
I would never presume it would be ok for people to hug the Queen.
我从来不认为我们可以拥抱女王。
Assume is to suppose something is true and will act as if it were true, but actually without proof.
Assume假设事实成立的意思，但事实上没有证据能证明假设真的成立。
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)
我假定她们会等我们(我不知道真的会不会，但我以她们会等作为前提)
I assumed that you had known the result. (no evidence, just based on my personal guess)
我假定你已经知道了结果(虽然我没证据，但我后续所有的行为都基于此假定)
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.
我觉得比较靠谱下周一铁路交通服务会恢复。但我们仍然可以考虑其他的交通方式作为备选项。
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