Logic For Hats

Three friends, Ann, Beatrice and Clara were playing a logic game together, with another friend Daisey as the game master.

At the start of the game, there were 5 hats. 3 of them were black, and the other 2 were white.

Ann, Beatrice and Clara stood in a circle, each of them with a blindfold on. Daisey placed a random hat on each of their heads. She kept the remaining 2 hats in a hidden place, before removing the blindfolds.

The 3 friends could see what hat the other friends are wearing, but could not see their own. They were curious to find out the colour of their hats, by using logical deduction. The following was a conversation between them, in order:

Ann : Beatrice does not know the colour of her hat!

Beatrice : Clara does not know the colour of her hat!

Clara : Ann knows the colour of her hat!

Assuming that each of the 3 friends were logical in their thinking, can it be deduced that all 3 friends were wearing black hats?

Hint: Ann said Beatrice does not know the colour of her hat. Therefore, Ann is sure that Beatrice did not see 2 white hats. How is Ann sure? It must be because Clara's hat is black! Now continue deducing the other friends hats.