Assuming that only a correct entry can win then the odds against winning, if you have sent in a correct solution, must depend on the number of correct entries, rather than the total number of entries.
Of course they don't open all of the entries. They open an entry and if it is correct it wins, if it has an error it is discarded. They go on doing that until they have found the required number of winners.
Presumably they then discard all the remaining unopened entries - unless they want to "harvest" all of the names and addresses to sell to direct marketing companies, which I would not put past them.