my probability that something like string theory is true would go way up after the detection of a Higgs boson

I'm not sure that this should be the case, as the Higgs is a Standard Model prediction and string theory is an attempt to extend that model. The accuracy of the former has little to say on whether the latter is sensible or accurate. For a concrete example, this is like allowing the accuracy of Newtonian Mechanics (via say some confirmed prediction about the existence of a planetary body based on anomalous orbital data) to influence your confidence in General Relativity before the latter had predicted Mercury's precession or the Michelson-Morley experiment had been done.

EDIT: Unless of course you were initially under the impression that there were flaws in the basic theory which would make the extension fall apart, which I just realized may have been the case for you regarding the Standard Model.