Speaking constitutes an important mode of asymptomatic transmission of COVID-19-type diseases. The typical public safety guidelines are based on symptomatic activities like coughing and sneezing, which may not hold for the spread of virus through speaking. Here we present computer simulations of the flows generated during two-people conversations over short time durations (of the order of 1-2 minutes). Simulations are carried out for different heights and lateral separations between the people. We find that the interaction between the speech "jets" generated by the two people plays a crucial role in determining the exposure of virions and the risk of infection; a small vertical/lateral separation is seen to enhance the risk of infection considerably. We use an improved method of calculating the probability of infection that includes the ingestion of virions through the eyes and mouth (along with inhalation through the nose) and present maps of infection probability for the set of parameters considered in the study. Based on our simulations, we suggest public health guidelines for minimizing the risk of infection in short conversations.