gives a nuance of 'probably' to sentences. It is more certain than かもしれない. It is more polite than (の)だろう. Note that it is very different from です+よ
明日は雨が降るでしょう。 Tomorrow, it will probably rain
今年の夏は恐らく涼しいのでしょう。 It's because this year, the summer will probably be cool.
with explanatory の
sometimes seen with explanatory の・んだ
denotes that you wonder whether or not something is the case.
it follows the rules of the explanatory の, with leading な.
あの人は==大丈夫なのでしょう==か。 I wonder whether or not that person is okay.
あれは本当に==食べ物::なのでしょう==か I wonder whether or not that is really food.
そんな高い鉛筆を彼が買うのでしょうか。 I wonder whether or not he would buy a pencil that is that expensive.