See, this is interesting. It doesn’t seem it from the outset. The basics of the information aren’t much to speak of. He’s just saying the letters are probably from Hamlet.
What’s interesting is that he doesn’t say that. He doesn’t say, “I bet these are from Hamlet.” Or “I wonder if Hamlet’s writing to me.” No.
There’s this extra bit of information here – a suggestion that he can’t imagine anyone else in the world writing to him. Which is odd, considering that he’s not from Denmark. Theoretically, he should be receiving letters from his family in, say, Italy. (I’m guessing Italy because of his name – but of course Marcellus and Barnardo and Francisco are all also Italian names and they seem more native to Elsinore.)
Doesn’t Horatio have any other friends? Does he not have any family? Why is no one writing to him but Hamlet? Does he have friends and family but he’s just not let them know where to find him? This raises a lot of questions for me about Horatio. What is going on with him? Why IS he in Elsinore?