FMEA itself is a deterministic way of classification of failures and consequences! however, if you put the amount of probability of any occurrence within the blocks in order to find the final reliability, it is considered as a probabilistic method.

FMEA is considered as probabilistic method of risk assessment. The design or process can be modified to avoid causes or reduce the probability that they will occur. If the concept can not be modified, the possibilities of detection must be studied more closely.

FMEA can be a part of probabilistic risk assessment. It can also be part of a quality concept. In its pure form, it has nothing to do with probability. It is purely deterministic

However, there is FMECA, which involves subjective assessment of probability of occurence of the failure modes. Also, there is FMEDA, which asks for failure rates or probability per demand of failure modes. Such FMEDA can be the source of data to quantify basic events in a fault tree analysis.

I would not try to argue, whether it is probabilistic or deterministic. I would argue, that it is a useful concept for any reliability or safety assesment.

Even if there are standards introducing FMEA approaches like IEC 60812, the FMEA is not a standard process. Thus, not always FMEA includes statistical information, nevertheless is always an useful analysis tool to make associations between causes and effects and consequently to identify the possible countermeasures to eliminate or at least mitigate undesired effects. However, according your question, if FMEA shall be used for risk assesment, it is forced to be a probabilistic approach because by definition risk is a combination of Severity (of the undesired effect) and Probability (of occurrence of the effect).

FMEA is usually considered as probabilistic method of risk assessment?

Check this document as an example