Use and explanation of "desho"

Hi,
I am currently studying Japanese and have so far finnished Genki I. I have come across the word "deshô" でしょう in the book, apparently often used when talking about weather reports, like, it will probably rain, it will probably be sun tomorrow, etc.

I got a reply from a hostel where they used the word でしょう in a sentence to ask about when I will be staying.　七月にいつでしょうか?　(Translated as "When will it be in July?" according to Google)
I would rather have used 七月にいつですか? (Translated as "When is it in July?" according to Google)

But as they use でしょう, I get the feeling they open up for my visiting dates are not fully decided yet?

This can also be used to make things about more roundabout, a bit more polite, instead of direct, so it is like asking "when would it be in July?" or "when in July might it be?" instead of asking "when in July is it?"

I am assuming that you did it specify the day of the month you intend to stay, so they decided to ask you that.
Was it 七月のいつでしょうか。?

I meant to write, you didn't specify the day ...

I agree with AK but would add that the polite use only works with でしょうか so in a question. You shouldn’t answer this question with 7月4日でしょう。but you could say 7月4日はいかがでしょうか。(this means, what about 4th ) although in this specific conversation it doesn’t make a lot of sense to ask a hotel about their suggestion for a day YOU want to stay there.

7月4日でしょう in turn sounds quite blunt to me. Something like, “well, it’s the 4th, ain’t it “

Enjoy studying Japanese!

7月4日でしょう。means "It will probably be July 4th."
If you haven't really decided the date but are just checking availability, this phrase would work (although it is a bit unnatural).

7月4日はいかがでしょうか。is commonly used to mean "Would it be available on July 4th?"
So this also works when checking availability.
When checking availability, this phrase is more commonly used than something like
7月4日です。which is not uncommon either.