probar vs intentar
'Try' covers two ideas. Probar is to test or taste. Intentar is to attempt.
probar
To try out, taste or test — you experience the thing to see what it's like.
Prueba esta salsa.
Try this sauce.
Tasting. The most common use.
¿Has probado el pulpo?
Have you tried octopus?
Experiencing something for the first time.
Prueba a reiniciar el ordenador.
Try restarting the computer.
Probar a + infinitive = try doing it as an experiment.
intentar
To attempt something, with effort and uncertain success.
Intenté llamarte tres veces.
I tried to call you three times.
Attempt. Intentar + infinitive.
Inténtalo otra vez.
Try again.
Intentar + lo = attempt it. A very common phrase.
Lo intentaré, pero no prometo nada.
I'll try, but I don't promise anything.
Intent to do, with no guarantee.
Tricky bit
'Probé hablar con ella' sounds like a test run. 'Intenté hablar con ella' is the attempt you mean. 'Tratar de' is a synonym of intentar and extremely common.