Always coming back to comments on this one. What does the sentence mean anyway? A masculine noun, some inanimate object that was left at home?
Why "it's probably home" isn't even more preferred translation, not only wrong? Can it include nouns like hund in this den meaning?
I see "den" in this sentence is as a non-living object, such as a key or a wallet. If people were talking about their pet or any family member, it's unlikely they'd refer to them as "it" or "that."
A: Fido was missing for two days.
B: He's probably home now.
A: My wife said she'd be out all afternoon.
B: She's probably home now.
Non-living objects require the preposition "at," e.g., "My key is probably at home."
The sentence, "It's probably home," sounds like someone opining about some kind of structure, or even a cave, e.g.,
A: Where do we sleep?
B: They said there was a cabin somewhere around here.
A: What do you think that is? (Pointing at a hovel.)
B: That's probably home.