If I inherit a house with a judgement against it will I inherit the debt of the judgement?

Is the judgement against the house, or against the (now deceased) owner of the house? If it's against the owner, then that debt passes on to the estate, and the estate assets can (and probably will) be auctioned to pay off the debt.

In a manner of speaking, yes. Any judgments against the house must be satisfied before you can take possession of the house. If the amount of the judgment(s) exceeds the value of the house, you cannot be forced to pay the difference out of your own pocket but it could mean no house for you to inherit as it would have to be sold to satisfy the judgment(s) unless you choose to satisfy the judgment(s) yourself, thereby enabling you to keep the house.

In probate the house should be sold to pay these debts, if there is no money in the estate to pay it.

If you wish to keep the house and not sell it, you will have to take on the debt to keep the house.