When does hh:mm = mm.ss?
Raku, 14 12 11 bytes

0+|*/.98334

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Since we know the bounds of the input, we can substitute a constant operation and a floor on the input in base 60.  That number by the way is around 1358/1381, which is the maximum the input differs from the output in base 60. There may be a smaller constant, or at least a smaller way to represent it. For reference, the shortest constant you can multiply by, rather than divide, is 1.01694.