"We now know"?
You can do better than that.
Actually
I can do better than that. Thanks for helping me to become a better man:
25-3905. Vacancies after primary election filled by party committee or district convention; governor and lieutenant governor vacancies filled by state party delegate convention. (a) When a vacancy occurs after a primary election in a party candidacy, such vacancy shall be filled by the party committee of the congressional district, county or state, as the case may be, except if the vacancy is in a party candidacy for a district office or for the office of member of the state board of education, it shall be filled by district convention held as provided in K.S.A. 25-3904, and amendments thereto, or as provided in K.S.A. 25-3904a, and amendments thereto, and except as otherwise provided in subsection (c). Such convention shall be called within 10 days of receipt of the notice that the vacancy has occurred or will occur. If only one political party nominates a candidate at the primary election and thereafter a vacancy occurs in such party candidacy, any political party may fill such vacancy in the manner specified in this section.
(b) In addition to other vacancies in party candidacies to which this section applies, this section shall also apply when a vacancy occurs in an office, and it is provided by law that such vacancy shall be filled by appointment until the next general election at which time a person is to be elected to fill the unexpired term, or words of like effect, and such vacancy occurs after the primary election.
If the race becomes too difficult for Roberts then he simply resigns and a party committee assigns a new candidate. Alternatively Roberts resigns his position immediately and Brownback appoints a new Senator, who can run as a sitting Senator.