the coin base (address of the receiver of coin on sucesfull hash) is part of a header that the miner will work on, so:
if solo mining, if each of tour miners connected directly to node and pass own coin base address- 0 chance. if each of the miners directly uses node and lets node set its coinbase, chances are very very slim (2^64 range) than youll hit the same nonce as negibour on same node (though this depends on node and miners, node could act as a pool and provide different nonce for each miner if they accept).
if mining in a pool, the coinbaise is always pools, and so every pool makes sure the nonce dont collide for each miner (oh and some one mentioned it doesnt matter for miners on pool to hit the same nonce, i think its opposite, because you are doing lower difficulty pow for the pool but still working on the real block hash, and thus the ones produce the actual full difficulty block hash, so very important to not dup work on a pool).
when two miners submit solution at the same time, its never the same solution (of cource if its for same pool on same nonce which all pools will want to prevent) its who finds any solution quicker, or i’ve just convinced so my self )