IMHO, Murkowski doesn’t expect to win but for reasons of personal bitterness and a sense of entitlement would rather split the vote just to defeat her political opponent. Republicans are now cursed with rogue politicians who out of sheer personal ambition refuse to follow the will of the voters in a primary election. Here in Florida we have the example of Charley Crist who knew he would roundly defeated by Marco Rubio in the Republican primary - so out of vanity, a personal quest for power and sheer ambition he chose to run as an Independent. For some of them I sincerely believe that destroying their rival by splitting the vote is actually more important than winning.
Reminds me of the guy who kills his ex because “if I can’t have her, nobody will have her!”