  Over the moduli space of pointed smooth algebraic curves, the projectivized
$k$-th Hodge bundle is the space of $k$-canonical divisors. The incidence loci
are defined by requiring the $k$-canonical divisors to have prescribed
multiplicities at the marked points. We compute the classes of the closure of
the incidence loci in the projectivized $k$-th Hodge bundle over the moduli
space of curves with rational tails. The classes are expressed as a linear
combination of tautological classes indexed by decorated stable graphs with
coefficients enumerating appropriate weightings. As a consequence, we obtain an
explicit expression for some relations in tautological rings of moduli of
curves with rational tails.
