"Where are the fitting rooms?"
Translation:¿Dónde están los probadores?
How would I know if 'probador' is masculine or feminine, since it does not end in 'o' or 'a'?
Unfortunately, you have to learn which is which (and not every word ending in o is masculine nor is every word ending in a feminine).
In general, nouns that end in -r will be masculine. There are exceptions, of course, but it's a decent rule of thumb while learning. https://www.123teachme.com/learn_spanish/grammar_gender_number_2