In this case, unless you are a professional gambler, you would claim the $12,500 as gambling winnings, and the $10,000 entry fee would qualify as gambling loss. Be advised, however, that the gambling loss may not offset the winnings entirely (or possibly not at all). In order to be deductible you must be able to itemize deductions on your return, which means your itemized deductions must be more than $12,000 if you are filing single and $24,000 if you are filing married.
Normally a prize would be considered as miscellaneous income, for which deductions are no longer allowed. But your winnings are directly tied to gambling, so they are correctly treated as gambling winnings.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"