Aggregators have an influential intermediary role to exploit the flexibility of prosumers like smart homes for procuring the required capacity of ancillary services to support power systems. Local generation and consumption uncertainties of prosumers affect their cost reduction objectives which in turn have a significant impact on the flexibility capacity provided by them. So, towards boosting the operational flexibility capacity in the market, the aggregator's bidding and remuneration frameworks should devise a valuing scheme of prosumers considering this impact to induce positive incentives relieving capacity uncertainties. This scheme, simultaneously, should observe data privacy concerns. To this end, this paper proposes a day-ahead distributed bidding strategy framework for an aggregator to participate in regulation and energy markets using a new rewarding scheme derived from a flexibility certainty valuing approach. This framework is developed within the Benders decomposition method, in which the aggregator performs valuing of prosumers in the master problem through their implicit information extracted from home energy management systems modeled in the subproblems. The performance of the framework to appropriately reward prosumers is presented through numerical results for an illustrative case study.