“The prime minister will likely go to Buckingham Palace Friday to meet the king”.
As PPs have said, this is not standard US English and not common usage in the US. "The PM is likely to go..." would be more likely (sorry) in a news broadcast than "the PM will probably go", but I see that as part of a general trend that language in the mainstream media in the USA right now is slightly more formal than the equivalent in the UK.
“I guess” instead of “I think”. "I guess" and "I think" have different meanings in US English. I agree that "I guess" is an Americanism, but the closest UK equivalent is probably "I suppose" (or maybe regionally "I reckon" or "I dare say", which are also used in the US.) "I guess" usually suggests a reluctance or hesitancy, whereas "I think" is declarative and decisive.