信じられないこと is not the content of 言葉. ~ことに is attached to verbs/adjectives that express emotion, and is used to express previously what the speaker thinks about the following thing.
e.g.
驚いたことに
残念なことに
興味深いことに
恐ろしいことに
ありがたいことに
Some linguists call this に 注釈副詞, i.e., adverb for annotation, but this is not officially accepted. Anyway, ~ことに means "this (= what I'm going to say) is ~, but...", so it close to ~ことだが in meaning. Thus, your example means "this is unbelievable, but..."