TheDepending on your location, the probation period always worksmay work both ways, soin which case it iswould be well within your rights to make use of it and leave your current employment for greener pastures (and twice the salary is indeed greener). You'll always have the option to resign according to the terms of your contract or local laws.
Employers often like to use the "not a cultural fit" excuse to fire someone in their probation period when they don't feel like giving an actual reason (and in order to protect themselves legally). But again, this can be used by both parties:
In your resignation tell your employer that you thank them for the opportunity, but that you don't fit into their culture.