First, I think you're looking for an adverb, not an adjective, but I 'm not sure what it might be. "Probably" and "might" aren't usually used together because they are too similar. "I might go to your house" is fine, and "I will probably go to your house" is fine, but "I probably might go to your house" sounds awkward. The only adjective i can think of with the meaning "that is not needed" is "unnecessary"(or "unnecessarily", if you need an adverb), but I can't see how it fits in your sentence. You could say "I might unnecessarily go to your house tomorrow."

Superfluous is another word that means "not needed" but you wouldn't use it in this case. Sorry I couldn't be of more help. Maybe another example would help or maybe it will just come to you randomly :) Anyway, keep up the good work.

"An adjective that I'm looking for is starting from "i" and has a meaning like "that is not needed". Sorry for poor explanation." Inessential? ""I probably might go to your house tomorrow". Probably is "the-adjective" here because probably and might have the same meaning." Sorry, I don't know what you mean here.