Based on what you have said, probate does not seem to be necessary. Probate is required to give someone legal authority to transfer title to the assets in a decedent's name. If all of the assets were jointly held or named you as beneficiary, then you would now be the sole owner, and there would be nothing left for the probate court to do.
In light of your husband's death, you should consult with an estate planning attorney to make sure that your estate planning is all in order and does not need to be adjusted.
I am very sorry for your loss.
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Mr. Frederick's answer was spot on. I would simply clarify that you want to send a copy of the death certificate to your husband's creditors not debtors. If your husband had debtors, that means that the debtors owed your husband money, not the other way around.
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