We investigate the extent to which we can infer social ties between a pair of users in an online social network Twitter, based on their common activities defined by the number of common celebrity profiles they are following. In this work, we analyze the list of celebrities that a set of Twitter users are following in December 2013 to infer the social ties that existed between these users till July 2009. We use two probabilistic models given by Kossinets et al. [Science, 2006] and Crandall et al. [PNAS, 2010] for this purpose. The model of Kossinets et al. is meant to give an upper bound for the probability of friendship between a pair of users, whereas the model by Crandall et al. is supposed to give an almost accurate estimate of the same. We observe that the model of Kossinets et al. is able to give an upper bound whereas the model given by Crandall et al. is unable to give an almost accurate estimate for our dataset. However, the model by Crandall et al. is observed to provide a correct estimate of the probability of friendship between the users when we consider following a particular type of celebrity profile, e.g. CEO, Author etc., as the activity of a user.