Part of your problem is you are thinking of the term literally "Dropped" third strike. When actually the rulebook term is a third strike not caught (or uncaught third strike). A ball can never be considered "caught" once it has hit the ground so therefore a strike three that hops into the catchers mitt is an uncaught third strike, batter may try for first (as long as it isn't occupied or there are two out).
-Josh
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