The purpose of a probationary period is for the company to ensure they haven't made a bad choice, before it becomes difficult to remove you. This is particularly common in the UK at medium-large businesses, for permanent contracts.
After a probation period, most companies policy involves multiple stages of goal-settings and performance plans; rather than trying to fire you on the spot (this is in part due to UK law on labor rights).
As such, if they realize a problem early - it is in their interest to end the employment instantly, rather than go through a prolonged (potentially longer than a year) process of writing you up, tracking your failings and firing you - all while being careful not to accused of wrongful termination.
For an internship, and also for many fixed-term contracts (especially if under 1 year length), as there is no risk of the business being stuck with you long-term - it's rare that they include probation periods.
Often the termination clauses in these contracts, is similar to probation in the first place, but even when it isn't - the worst case for the business is they simply pay you till the end of your contract. There's simply not the same risk of getting stuck in a quagmire of HR policy and legal obligation, as for a permanent role.
So to answer directly;
For an internship, this is expected. Just accept the contract if you're happy with it. If they wanted a probation period - they should have written one into the contract.