恐(おそ)らくProbably, Perhaps, (Most) likely, (I) fear that

恐(おそ)らく is an adverb which originally stems from the conjugation of the yodan verb, 恐(おそ)る 'to fear'. In most cases, 恐(おそ)らく is simply used as a formal way to say 'probably', or 'perhaps', and is usually partnered with other structures of conjecture such as だろう, かもしれない, etc.

As 恐(おそ)らく behaves adverbially, it will most often appear at the beginning of sentences before a statement of conjecture is made.

Although 恐(おそ)らく can, and often does, carry the meaning of 'I fear that (A)', it isn't necessarily always used in relation to negative things. In the case of this particular grammar pattern, the main nuance that 'I fear that (A)' conveys is modesty on behalf of the speaker in that they fear their assumption may be right, given the available information.

Fun-fact

Yodan, or 四段活用(よだんかつよう) verbs are a type of classical-Japanese verb that have primarily been replaced by godan (う-Verbs) in modern day Japanese.