Bayou Classic 500-580, 2.5-in diameter Grill Thermometer

Can anyone answer how long the probe is on this thermometer? I need a 3 to 4 inch probe with a 2.5 inch diameter.

any problems with water build up or condensation?

Will this work on a large big green egg ?

Is this made to rest directly on the grate, inside the grill? Thanks.