What would be the difference between 你认识不认识他？ and 你认不认识他？ Are they the translated with the same "Do you probably know him?
Both sentence means "do you know him?". "Probably" is not necessary, because these are very direct ways to ask questions.
For you interest, an even more concise version is "你认识他不？"
Well, all these expression are spoken language because of the function of these sentences.
For more details of how a complete sentence is changed into correct shorter versions, please see the diagram as below:
The most complete version "你是认识他还是不认识他？" is almost never used unless in an interrogation. It sounds almost like "你tm到底是认识他还是不认识他啊！？", which is rude. Extra words tend to show superfluous emotion like anger or impatience. I put it here because you can see how other shorten versions can be related to this origin. Other expressions are fine and often used.