The best replacement for probit is logit.

The best alternatives to probit are rated as following:
★★★★★  logit
★★  logit regression
★★  ols
★★  logistic
★★  linear probability model
★  logistic regression
★  logit stata
  ordered probit
  lpm
  ordered logit
  multinomial logit

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Speaking about probit, one probably shouldn't forget about fixed effects.

Other search terms related to probit and their ratings are:
★★★★★ fixed effects
★★★★ sample selection
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probit
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