No, the encryption algorithm used in one-time pad encryption does not need to be either probabilistic or random. The most common historical OTP algorithm is a simple substitution cypher. In digital encryption, the OTP algorithm most commonly used is XOR. Neither algorithm introduces any uncertainty. It's the key material that must be random. And how that key material is generated is critical. It must be derived from a cryptographically secure source of randomness.
Acceptable sources of randomness are surprisingly difficult to come by. Computers, despite their reputations, are designed to be precisely accurate and repeatable. The most secure random numbers come from hardware using stochastic processes such as the timing of radioactive decay, thermal component noise, and other such sources. Most commercial computers don't contain a hardware random number generator, however, so they collect different bits of things that are considered hard to predict, and combine them together into a large collection of hard-to-predict bits. This process is often called "gathering entropy". To stretch a small number of hard-to-predict bits into a usefully large number of random bits, pseudo-random number generation algorithms are sometimes used, which accept the small number of bits as a seed and produce a larger number of bits of output. Pseudo-random number generators are often built from proven secure cryptographic routines such as AES or SHA-2.
And if you're using AES to stretch a small number of bits into a long string of bits, you are essentially encrypting with AES, starting with a random number as the key. That's why a "one time pad" using a computer-generated key stream is rarely as effective as an actual one-time pad. The good news is that it's still as effective as AES, which is considered strong.
The bad news is that because people don't understand randomness very well, they think that any series of values they themselves can't predict will serve as an adequate key for a one-time pad.
To help understand why one-time pads work the way they do, I recommend studying real world attacks. One of the best documented attacks is the Venona project, recently declassified by the NSA, where they deciphered the one-time pads used by Soviet spies. The reason they were able to decipher them is that Soviet agents actually reused the keys, turning them into two-time pads. It is generally accepted that because generating the key material was tedious, time consuming, and expensive, and distributing it securely was extremely risky and difficult, that they economized by reusing the keys. That led to the break in the code, which in turn identified such notorious spies as Julius and Ethel Rosenberg and David Greenglass, and provided absolute proof of their guilt in delivering the secrets of the atomic bomb to the Soviet Union.
That cryptanalysis of course revealed the keys of the one-time pads, and those were also studied. It was determined from the distribution of the letters used that a typist simply banged back and forth on a keyboard, from one side to the other, to generate the keys. It's hard to imagine a more tedious job.