"Tabun" and "darou"

Hi! I understand that たぶん and だろう have the same meaning, i.e. maybe/probably/perhaps but why can they appear in the same sentence as mentioned below? Isn't it redundant?

このみせはりょうりがたぶんおいしいだろうとおもいます。

Is the sentence below correct?
あのひとはうたがじょうずだろうとおもいます。

Pls kindly advise on the above mentioned.
Many many thanks!

I don't see a big problem with the way you wrote the sentences.

~かもしれない is also a way of saying "probably" or "might"

If you hurry, you might make it!
急いだら、間に合うかもしれない！
you can shorten it to かも informally

Yes it is redundant.
It is like "I think perhaps this restaurant may be good".
Instead of "このみせはりょうりがたぶんおいしいだろうとおもいます。", say "このみせはりょうりがたぶんおいしいとおもいます。"
It is ok to say "あのひとはうたがじょうずだろうとおもいます。"