The text says "I probably have a great relationship with Kim Jong Un" but it does sound like he says "I'd probably have a great relationship...". But if he did say "I'd" it seems like it would have been followed by an "if"...for example "I'd probably have a great relationship with Kim Jong Un IF we weren't always threatening to blow eachother up!" Sorry if thats confusing but I did my best to answer your question!

I would use "I probably have". According to dictionary I'd short for I had. "I'd agreed to go" I'd short for I should or I would "I'd like a bath"