With respect to the question of the IRS coming after you for your ex husband's tax debt, unfortunately, the fact that he agreed to pay the tax in the marital settlement agreement will not be binding on the IRS. You may try responding to the IRS by providing them with a copy of the marital settlement agreement to see what they do. However, agreements between taxpayers have no effect on the application of the Internal Revenue Code.
You may consider filing an innocent spouse relief request with the IRS. In the request, you could ask for equitable relief from the liability by arguing that your ex agreed to pay the tax as part of the settlement, that he died shortly thereafter and then the estate (to the extent there was any value in the estate) was improperly divested of value. This may get you relief from the debt based on "equitable principles" and may encourage the IRS to pursue the beneficiaries of the estate for the recovery of the tax (instead of you).
If innocent spouse equitable relief is not your answer another option exists. You may have heard of the Offer in Compromise program. This program allows the IRS to cut a deal (i.e. settle for less than the full amount of the debt). There are three ways to ask for a compromise: financial hardship, doubt as to your liability for the debt and "other equitable reasons." Each requires the completion and submission of IRS forms.
As you said you are unable to pay, perhaps the financial hardship is appropriate. If so, you need to prepare a detailed financial statements from which the IRS will determine if a deal/compromise is appropriate.
As for your question on filing probate, that will likely be a question of state law where your ex lived. It is unrelated to how the IRS will handle your case but might be a way for you to recover something. You may want to contact a probate attorney in your state to learn a little more about the process. If the potential cost of an attorney is a concern, consider contacting the State Bar to find out what type of programs may exist for getting information or other legal assistance.