Wrong overload selected when implicity converting to a const type

Consider the code below:

#include <iostream>

// General overload using a template
template <typename SomeType>
void some_func(const SomeType p) {
    std::cout << "Using the general function" << std::endl;

// Specific overload, accepting a 'const double*' type
void some_func(const double* p) {
    std::cout << "Using the function accepting a const double*" << std::endl;

int main() {
    // This one uses the specific overload, as expected
    const double *a = new double(1.1);
    delete a;
    // This one uses the general function rather than the second overload
    double *b = new double(1.1);
    delete b;
    return 0;

In this piece of code, there are two overloads of the some_func function. The first one is the most general overload, using a template to capture practically any type. The second overload is a specific overload, accepting a const double* type as its argument.

In the main function, I first create the variable a of type const double*. When supplying a to some_func, the second overload is selected. This is as expected. Secondly, I create a variable b of type double* (so no const). When supplying the variable b to some_func, it selects the first overload. I would’ve expected it to select the second overload, as (I think) it should be able to implicitly convert a type double* to const double*. Why does it select the first overload rather than the second overload in this case?

For completeness, this is the output of the program:

$ g++ main.cpp
$ ./a.out
Using the function accepting a const double*
Using the general function


During template instantiation, this const SomeType p would turn into double* const p which is a better match than const double*. That is, the template’s parameter would become a const-pointer to mutable data.
In the template function, you can actually modify the data through that pointer, so it can be assumed it is a better match.
If you change const SomeType p to const SomeType* p, the specific overload will be selected.