Unless the terminated employee has completed more than 6 or 12 months service with the employer at the time of termination (12 months in the case of a small business with fewer than 15 employees, otherwise 6 months – this is referred to as the "qualifying period"), the employee will generally not be eligible to lodge a claim for unfair dismissal. In the vast majority of cases, probation periods are of 3 or 6 months duration, so in these cases terminated employees will not, but for exceptional circumstances, be able to claim unfair dismissal.
As a result, it's generally pretty safe during the probation period to "shortcut" the performance management process in terms of providing warnings, formal meetings, review periods etc.. While it's best practice of course to ensure your new employee clearly understands your expectations, is given reasonable support to meet those expectations, including coaching if performance/conduct issues arise, it is generally sufficient during a probation period to issue a termination letter, which should clearly indicate the employee's last day of employment. It is also important that the person is given appropriate notice of termination (this will generally be 1 week, but be sure to check any applicable awards, agreements, contracts and organisation policies).
It is important to note that the termination cannot be for discriminatory reasons, or other reasons such as the employee joining a union, making a workplace complaint, querying their pay and other conditions of employment, or other reasons covered by the general protections provisions of the Fair Work Act. An employee terminated for these reasons may be able to lodge a claim against their termination, regardless of the duration of their employment.
Note that this article is current at the time of writing, presents general information only and should not be considered formal or legal advice. If you think your business may be impacted by these issues, you should seek additional information/support, to ensure your specific circumstances are accounted for.