Excel - Selecting Only One Max Value

I have a dataset that looks like below. Column E would be my formula column. I would like Column E to read "Max" for the row where the ID contains the max probability for that state. If two IDs for the same State have the same probability, as in Maryland, I want "Max" to show for the ID with the nearest Date. If two IDs match on both Probability and Date, then I want "Max" to appear for only one ID within each group of States.

    Column A       Column B     Column C    Column D    Column E
    State        Probability       Date        ID       Formula Field
    California        10%       12/31/2016    123   
    California        20%       1/7/2017      129   
    California        23%       1/14/2017     135       Max
    Colorado          26%       1/21/2017     141   
    Colorado          38%       12/31/2016    147       Max
    Illinois          44%       1/14/2017     153       Max
    Illinois          44%       1/14/2017     159   
    Illinois          20%       1/21/2017     165   
    Illinois          35%       1/28/2017     171   
    Maryland          41%       2/4/2017      177   
    Maryland          41%       12/31/2016    183       Max
    Maryland          35%       1/7/2017      189   
    Michigan          20%       1/14/2017     195   
    Michigan          35%       1/21/2017     201   
    Michigan          38%       1/28/2017     207       Max
    West Virginia     41%       2/4/2017      213   
    West Virginia     44%       2/11/2017     219       Max