You could add in a simple if statement and raise an Error if the number isn't within the range you're expecting

while True:
    try:
        number1 = int(input('Number1: '))
        if number1 < 1 or number1 > 10:
            raise ValueError #this will send it to the print message and back to the input option
        break
    except ValueError:
        print("Invalid integer. The number must be in the range of 1-10.")

Here is how you can do it with regular expressions.
Just check if input string containing only allowed chars.

import re

def is_valid_name(str):
    pattern = "^[a-zA-Z\ \.\-]+$"
    return bool(re.search(pattern,str))

print is_valid_name("Bob Smith")
print is_valid_name("Dr. Smith")
print is_valid_name("Anne-Marie")
print is_valid_name("Anne!Marie")

Get the input then check if the input is valid to your constraint (e.g. via an if condition). If it is not valid repeat the input (probably with notifiyng the user what was wrong with the input before) (e.g. with a while loop).

Does the following help?

import math
from scipy.optimize import minimize,NonlinearConstraint

def fmin(x):
# this is the function you are minimizing
# in your case this function just returns x
    return x

def fprob(x):
# this is the function defining your probability as a function of x
# this function is maximized at x=3, and its max value is 1
  return math.exp(-(x-3)*(x-3))

# these are your nonlinear constraints
# since you want to find input such that your probability is > 0.8
# the lower limit is 0.8. Since probabilty cannot be >1, upper limit is 1
nlc  = NonlinearConstraint(fprob,0.8,1)

# the zero is your initial guess
res = minimize(fmin,0,method='SLSQP',constraints=nlc)

# this is your answer
print(f'{res.x=}')