Would you agree that given exact info of conditions one can objectively assign concrete probability? That would give objectivity to it.
Definition of "real" for daily life is hard (impossible?). I would say "probabilities" are as real as other useful constructs that impact our lifes. Examples would be "countries" and "laws".
Is country X real? (what if it is recognised only by 1 UN nation?) Is law real? Is law real in <insert-country-in-turmoil-with-very-very-selective-enforcement>.
Are particles on the quantum level real or just mathematical constructs that describe what we can observe, just like probability is?
I don't think "exact info of conditions" is objective or coherent. This pre-supposes there's an external universe with exact conditions that produces our experiences, but there's no way to distinguish this possiblity from other possibilities (like a multiverse, for instance.) This lack of ability to distinguish, in my ontology, makes the distinction meaningless. Yours may differ.